<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">K.K. KENZHEBAEV</style></author><author><style face="normal" font="default" size="100%">A.N. STANZHYTSKYI</style></author><author><style face="normal" font="default" size="100%">A.O. TSUKANOVA</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">EXISTENCE AND UNIQUENESS RESULTS, THE MARKOVIAN PROPERTY OF SOLUTION FOR A NEUTRAL DELAY STOCHASTIC REACTION-DIFFUSION EQUATION IN ENTIRE SPACE</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34K40</style></keyword><keyword><style  face="normal" font="default" size="100%">34K50</style></keyword><keyword><style  face="normal" font="default" size="100%">60H15</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2019</style></year><pub-dates><date><style  face="normal" font="default" size="100%">10/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/28/1/2.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">28</style></volume><pages><style face="normal" font="default" size="100%">28</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;We establish results, concerning existence, uniqueness, and continuous dependence on an initial datum of a mild solution for neutral stochastic integro-differential equations with variable time delay of reaction-diffusion type. We also establish the Markovian property of this solution. Herewith our emphasis is on unbounded domain $\{x \in \mathbb{R}^{d}\}$.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><section><style face="normal" font="default" size="100%">19</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">SUPAKNAREE SATTASO</style></author><author><style face="normal" font="default" size="100%">KAMSING NONLAOPON</style></author><author><style face="normal" font="default" size="100%">HWAJOON KIM</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">FURTHER PROPERTIES OF LAPLACE-TYPE INTEGRAL TRANSFORMS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34A25</style></keyword><keyword><style  face="normal" font="default" size="100%">34A35</style></keyword><keyword><style  face="normal" font="default" size="100%">44A05</style></keyword><keyword><style  face="normal" font="default" size="100%">44A10</style></keyword><keyword><style  face="normal" font="default" size="100%">44A20</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2019</style></year><pub-dates><date><style  face="normal" font="default" size="100%">01/2019</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/28/1/12.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">28</style></volume><pages><style face="normal" font="default" size="100%">22</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;In this paper, we study some properties of Laplace-type integral&amp;nbsp;transforms, which have been introduced as a computational tool for solving differential&amp;nbsp;equations, and present some examples to illustrate the effectiveness of its applicability.&amp;nbsp;Moreover, we give an example that cannot be solved by Laplace, Sumudu, and Elzaki&amp;nbsp;transforms, but it can be solved by Laplace-type integral transforms; this means&lt;br /&gt;
that Laplace-type integral transforms are a powerful tool for solving some differential&amp;nbsp;equations with variable coefficients.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><section><style face="normal" font="default" size="100%">195</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">NIKOLAY KYURKCHIEV</style></author><author><style face="normal" font="default" size="100%">ANTON ILIEV</style></author><author><style face="normal" font="default" size="100%">ASEN RAHNEV</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A NEW CLASS OF ACTIVATION FUNCTIONS BASED ON THE CORRECTING AMENDMENTS OF GOMPERTZ–MAKEHAM TYPE</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">41A46</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2019</style></year><pub-dates><date><style  face="normal" font="default" size="100%">02.2019</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/28/2/2.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">28</style></volume><pages><style face="normal" font="default" size="100%">16</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;We will explore the interesting methodological task for constructing&amp;nbsp;new activation functions using ”correcting amendments” of ”Gompertz-Makeham-type” (GMAF). We also define the new family of recurrence generated activation&amp;nbsp;functions based on ”Gompertz–Makeham correction” - (RGGMAF).&lt;/p&gt;

&lt;p class=&quot;rtejustify&quot;&gt;We prove upper and lower estimates for the Hausdorff approximation of the sign&amp;nbsp;function by means of this new class of parametric activation functions - (RGGMAF).&amp;nbsp;Numerical examples, illustrating our results are given.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">2</style></issue><section><style face="normal" font="default" size="100%">243</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ANTON ILIEV</style></author><author><style face="normal" font="default" size="100%">NIKOLAY KYURKCHIEV</style></author><author><style face="normal" font="default" size="100%">ASEN RAHNEV</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A NEW IMPROVEMENT OF TEMBHURNE-SATHE MODIFICATION OF EUCLIDEAN ALGORITHM FOR GREATEST COMMON DIVISOR. IV</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">11A05</style></keyword><keyword><style  face="normal" font="default" size="100%">68W01</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2019</style></year><pub-dates><date><style  face="normal" font="default" size="100%">01/2019</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/28/1/8.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">28</style></volume><pages><style face="normal" font="default" size="100%">10</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;In this note we gave new interpretation of Tembhurne-Sathe modification of Euclidean algorithm for calculation of greatest common divisor (GCD). Our&amp;nbsp;results are different optimized ways of approaches presented in [1]–[26], [44]–[68]. Our&amp;nbsp;approach is about 9% and 69% faster than Tembhurne-Sathe algorithm in iterative&amp;nbsp;and recursive implementations respectively. For computer implementation Visual C#&amp;nbsp;2017 programming environment is used.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><section><style face="normal" font="default" size="100%">143</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">EKKACHAI KUNNAWUTTIPREECHACHAN</style></author><author><style face="normal" font="default" size="100%">CHANON PROMSAKON</style></author><author><style face="normal" font="default" size="100%">THANIN SITTHIWIRATTHAM</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">NONLOCAL FRACTIONAL SUM BOUNDARY VALUE PROBLEM FOR A COUPLED SYSTEM OF FRACTIONAL SUM-DIFFERENCE EQUATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">39A05</style></keyword><keyword><style  face="normal" font="default" size="100%">39A12</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2019</style></year><pub-dates><date><style  face="normal" font="default" size="100%">01/2019</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/28/1/5.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">28</style></volume><pages><style face="normal" font="default" size="100%">20</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;In this article, we study the existence and uniqueness result for a&amp;nbsp;coupled system of fractional sum-difference equations with nonlocal fractional sum&amp;nbsp;boundary conditions, by using the Banach’s fixed point theorem. Finally, we present&amp;nbsp;an example to show the result of this paper.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><section><style face="normal" font="default" size="100%">73</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">SVETOSLAV MARKOV</style></author><author><style face="normal" font="default" size="100%">ANTON ILIEV</style></author><author><style face="normal" font="default" size="100%">ASEN RAHNEV3</style></author><author><style face="normal" font="default" size="100%">NIKOLAY KYURKCHIEV</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A NOTE ON THE THREE–STAGE GROWTH MODEL</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">41A46</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2019</style></year><pub-dates><date><style  face="normal" font="default" size="100%">11/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/28/1/4.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">28</style></volume><pages><style face="normal" font="default" size="100%">10</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;In this paper we study the one–sided Hausdorff approximation of&amp;nbsp;the generalized cut function by sigmoidal modified three–stage growth model. The&amp;nbsp;model has a certain right of existence insofar as the theory of sigmoidal functions&amp;nbsp;is well developed. The estimates of the value of the best Hausdorff approximation&amp;nbsp;obtained in this article can be used in practice as one possible additional criterion&amp;nbsp;in ”saturation” study. We examine the small data for modeling the growth of red&amp;nbsp;abalone Haliotis Rufescens in Northern California. Numerical examples are presented&lt;br /&gt;
using &lt;em&gt;CAS MATHEMATICA&lt;/em&gt;.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><section><style face="normal" font="default" size="100%">63</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">MEIHUA DONG</style></author><author><style face="normal" font="default" size="100%">SANGJIN KIM</style></author><author><style face="normal" font="default" size="100%">JIANDONG YIN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">GROUP ACTIONS WITH TOPOLOGICALLY STABLE MEASURES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">37C85</style></keyword><keyword><style  face="normal" font="default" size="100%">54H20</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">01/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://www.acadsol.eu/dsa/articles/27/1/10.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">27</style></volume><pages><style face="normal" font="default" size="100%">16</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;We prove that if an action $T$ of a finitely generated group $G$ on a compact metric space $X$ is measure expansive and has the measure shadowing property then it is measure topologically stable. This represents a measurable version of the main result in [4]. Moreover we prove that if $G$ is a finitely generated virtually nilpotent group and there exists $g \in G$ such that $T_g$ is expansive and has the invariant measure shadowing property then $T$ is invariant measure topologically stable. Finally we show that minimal actions approximated by periodic ones have no topologically stable measures.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><section><style face="normal" font="default" size="100%">185</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">SVETOSLAV MARKOV</style></author><author><style face="normal" font="default" size="100%">NIKOLAY KYURKCHIEV</style></author><author><style face="normal" font="default" size="100%">ANTON ILIEV</style></author><author><style face="normal" font="default" size="100%">ASEN RAHNEV</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A NOTE ON THE LOG–LOGISTIC AND TRANSMUTED LOG–LOGISTIC MODELS. SOME APPLICATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">41A46</style></keyword><keyword><style  face="normal" font="default" size="100%">68N30</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">07/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/27/3/9.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">27</style></volume><pages><style face="normal" font="default" size="100%">16</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;The Hausdorff approximation of the shifted Heaviside function by&amp;nbsp;Log-logistic and quadratic transmuted Log-logistic sigmoid functions is investigated&amp;nbsp;and an expression for the error of the best approximation is obtained. The results of&amp;nbsp;numerical examples performed in the programming environmentMathematica confirm&amp;nbsp;our theoretical conclusions. Some applications in the field of biochemical processes&amp;nbsp;and debugging theory are also explored.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">3</style></issue><section><style face="normal" font="default" size="100%">593</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">PEKKA KOSUNEN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">PERIODIC ORBITS OF QUADRATIC POLYNOMIALS OF PERIODS SIX AND SEVEN</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">30D05</style></keyword><keyword><style  face="normal" font="default" size="100%">37F10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">01/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/27/1/4.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">27</style></volume><pages><style face="normal" font="default" size="100%">44</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;The dynamics of quadratic polynomials is commonly studied by using&amp;nbsp;the family of maps $f_c (x) = x^2&amp;nbsp;+ c$, where $c\in C$. In this paper we form equations of&amp;nbsp;periodic orbits of periods six and seven on a new $(u, v)$-plane and consider also the&amp;nbsp;corresponding equations on the $(x, y)$-plane. The new $(u, v)$-model produces equations&amp;nbsp;for the periods six and seven with significantly lower degree than the ones obtained&amp;nbsp;by the previous models which enables us to find their solutions.&lt;br /&gt;
&amp;nbsp;&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><section><style face="normal" font="default" size="100%">63</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">HWAJOON KIM</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">THE SOLUTION OF THE HEAT EQUATION WITHOUT BOUNDARY CONDITIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">35A22</style></keyword><keyword><style  face="normal" font="default" size="100%">44A10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">07/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/27/3/10.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">27</style></volume><pages><style face="normal" font="default" size="100%">10</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;We would like to propose the solution of the heat equation without&amp;nbsp;boundary conditions. The methodology used is Laplace transform approach, and the&amp;nbsp;transform can be changed another ones. This attempt is more advanced than the&amp;nbsp;existing method and has a meaning in that it is approached in a general way without&amp;nbsp;restricting the boundary conditions. The solution of heat equation is presented by&amp;nbsp;using the property of integrability of transform.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">3</style></issue><section><style face="normal" font="default" size="100%">653</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">RATINAN BOONKLURB</style></author><author><style face="normal" font="default" size="100%">KEERATI KAEWRAK</style></author><author><style face="normal" font="default" size="100%">TAWIKAN TREEYAPRASERT</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">SOLUTION PROFILES BEYOND QUENCHING FOR SINGULAR SEMILINEAR PARABOLIC PROBLEMS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">35K35</style></keyword><keyword><style  face="normal" font="default" size="100%">35K57</style></keyword><keyword><style  face="normal" font="default" size="100%">35K61</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">08/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/27/3/15.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">27</style></volume><pages><style face="normal" font="default" size="100%">18</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;Let $T\leq\infty,~a&amp;gt;0,$ $0&amp;lt;r&amp;lt;1,~D=(0,a),~\Omega=D\times(0,T]$ and $\chi(S)$ be&amp;nbsp;the characteristic function of the set $S$. This article studies the&amp;nbsp;steady-state solution after quenching has occured of the semilinear parabolic&amp;nbsp;equation with singularity&lt;br /&gt;
\begin{align*}&lt;br /&gt;
&amp;amp; &amp;nbsp;u_{t}-u_{xx}-\frac{r}{x}u_{x}=f(u)\chi(\{u&amp;lt;c\})~\text{in}~\Omega,\\&lt;br /&gt;
&amp;amp; &amp;nbsp;u(x,0)=0~\text{on}~\bar{D},\\&lt;br /&gt;
&amp;amp; &amp;nbsp;u(0,t)=0=u(a,t)~\text{for}~0&amp;lt;t&amp;lt;T.&lt;br /&gt;
\end{align*}&lt;/p&gt;

&lt;p class=&quot;rtejustify&quot;&gt;It is shown that as $t$ tends to $\infty$, all weak solutions $u\left(x,t\right) &amp;nbsp;$ tend to a unique steady-state solution $U(x)\text{ for }\ 0&amp;lt;{{b}_{s}^{\ast}}\leq x\leq{{B}_{s}^{\ast}}&amp;lt;a$. The numerical methods are&amp;nbsp;developed for computing ${{b}_{s}^{\ast}}$ and ${{B}_{s}^{\ast}}$.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">3</style></issue><section><style face="normal" font="default" size="100%">673</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">SNEZHANA HRISTOVA</style></author><author><style face="normal" font="default" size="100%">PETER KOPANOV</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">STABILITY OF NEURAL NETWORKS WITH RANDOM IMPULSES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34A37</style></keyword><keyword><style  face="normal" font="default" size="100%">34D20</style></keyword><keyword><style  face="normal" font="default" size="100%">34F99</style></keyword><keyword><style  face="normal" font="default" size="100%">92B20</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">10/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/27/4/7.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">27</style></volume><pages><style face="normal" font="default" size="100%">12</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;One of the main properties of solutions of neural networks is stability&amp;nbsp;and often the direct Lyapunov method is used to study stability properties. We consider the Hopfield’s graded response neural network in the case when the neurons are&amp;nbsp;subject to a certain impulsive state displacement at random exponentially distributed&amp;nbsp;moments. It changes significantly the behavior of the solutions because they are not&amp;nbsp;deterministic ones but they are stochastic processes. We examine the stability of the&amp;nbsp;equilibrium of the model. Some sufficient conditions for p-moment stability of equilibrium of neural networks with time varying self-regulating parameters of all units&amp;nbsp;and time varying functions of the connection between two neurons in the network are&amp;nbsp;obtained. These sufficient conditions are explicitly expressed in terms of the parameters of the system and hence they are easily verifiable. We illustrate our theory on&amp;nbsp;a particular nonlinear neural network.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">4</style></issue><section><style face="normal" font="default" size="100%">791</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">LINA MA</style></author><author><style face="normal" font="default" size="100%">D. KANNAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">VALUATION OF REVERSE MORTGAGE WITH DEPENDENT JOINT LIVES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">joint annuity</style></keyword><keyword><style  face="normal" font="default" size="100%">jump-diffusion</style></keyword><keyword><style  face="normal" font="default" size="100%">lifetime model</style></keyword><keyword><style  face="normal" font="default" size="100%">reverse mortgage</style></keyword><keyword><style  face="normal" font="default" size="100%">valuation</style></keyword><keyword><style  face="normal" font="default" size="100%">Vasicek model</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">12/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/27/4/13.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">27</style></volume><pages><style face="normal" font="default" size="100%">32</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;Utilizing the principle of balance between expected gain and expected&amp;nbsp;payment, this work obtains the analytic valuation formula for reverse mortgage. In&amp;nbsp;particular, we provide the formulas for the lump sum payment, joint annuity, increasing (decreasing) annuity, and level annuity of reverse mortgage. We also derive the&amp;nbsp;valuation equation that the variable payment annuities satisfy. We then discuss the&amp;nbsp;monotonicity of the lump sum, annuity, and annuity payment factors with respect to&amp;nbsp;the parameters associated with the home price and the interest rate model. Finally,&amp;nbsp;we analyze the sensitivity of the joint annuity with respect to the parameters associated with the home price, interest rate, and lifetime model. The numerical results&amp;nbsp;show that the average return of home price exerts a dominating influence on the joint&amp;nbsp;annuity, followed by the mean reversion level of interest rate, and both of them have&amp;nbsp;stronger impact on the annuities of younger applicants than those of older applicants.&amp;nbsp;Meanwhile, the initial age of male and that of female produce asymmetrical effect&amp;nbsp;on the joint annuity. Remarkably, the dependence of joint-lifetime significantly affect&amp;nbsp;the joint annuity value. In case that the male and female initial ages are both less&amp;nbsp;than 80 years old, annuity values on average increase&amp;nbsp; approximately 4.5%, and the&amp;nbsp;greatest increment of annuity value approaches 9%.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">4</style></issue><section><style face="normal" font="default" size="100%">895</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ZEYNEP KAYAR</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">AN EXISTENCE AND UNIQUENESS RESULT FOR LINEAR SEQUENTIAL FRACTIONAL BOUNDARY VALUE PROBLEMS (BVPS) VIA LYAPUNOV TYPE INEQUALITY</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34A08</style></keyword><keyword><style  face="normal" font="default" size="100%">34B05</style></keyword><keyword><style  face="normal" font="default" size="100%">34C10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/26/1/8.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">10</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;A sufficient condition for the existence and uniqueness of solution of nonhomogenous fractional boundary value problem involving sequential fractional derivative of Riemann Liouville type is established by using a new Lyapunov type inequality and disconjugacy criterion. Green’s function and some of its properties are also presented. Our approach is quite new and to the best of our knowledge, the uniqueness of solution of nonhomogenous fractional boundary value problems is proved by employing Lyapunov type inequality for the first time and this Lyapunov type inequality improves and generalizes the previous ones.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><section><style face="normal" font="default" size="100%">147</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">LINA MA</style></author><author><style face="normal" font="default" size="100%">JINGXIAO ZHANG</style></author><author><style face="normal" font="default" size="100%">D. KANNAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">FAIR PRICING OF REVERSE MORTGAGE WITHOUT REDEMPTION RIGHT</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/26/34/6.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">25</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We derive in this article the pricing of a reverse mortgage without redemption right. In this, the underlying model employs a jump-diffusion process to represent the dynamics of the housing price, the Vasicek model to drive the instantaneous interest rate, and the force mortality model to describe the longevity risk. The said pricing is based on the Principle of Balance between the expected gain and expected payment. We compute the expected gain and the expected payment respectively under the continuous and discrete framework. We also present, with the above model, explicit formulas for the increasing (or decreasing) perpetual annuity and the level perpetual annuity. Furthermore, we discuss the monotonicity property of the annuities, lump sum, and annuity payment factors with respect to the parameters associated with the house price, the interest rate, and the force of mortality model. Finally, some numerical results for the lump sum, the annuity, and the annuity payment factors are presented, and also the sensitivity with respect to the above parameters is discussed. Based on the average change rate, we evaluate all parameters’ degree of impact on the annuity, the lump sum, and the annuity payment factors.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">3&amp;4</style></issue><section><style face="normal" font="default" size="100%">473</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">E KORKMAZ</style></author><author><style face="normal" font="default" size="100%">C TUNC</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">INEQUALITIES AND EXPONENTIAL DECAY OF CERTAIN DIFFERENTIAL EQUATIONS OF FIRST ORDER IN TIME VARYING DELAY</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34C11</style></keyword><keyword><style  face="normal" font="default" size="100%">34D20</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/26/1/9.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">10</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, we give sufficient conditions to guarantee exponential decay of solutions to zero of the time varying delay differential equation of first order. By using the LyapunovKrasovskii functional approach, we establish new results on the exponential decay of solutions, which include and improve some related results in the literature.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><section><style face="normal" font="default" size="100%">157</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">MALIK MUSLIM</style></author><author><style face="normal" font="default" size="100%">AVADHESH KUMAR</style></author><author><style face="normal" font="default" size="100%">MICHAL FEÇKAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">PERIODIC SOLUTIONS TO SECOND ORDER NONLINEAR DIFFERENTIAL EQUATIONS WITH NON-INSTANTANEOUS IMPULSES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34G20</style></keyword><keyword><style  face="normal" font="default" size="100%">34K30</style></keyword><keyword><style  face="normal" font="default" size="100%">34K45</style></keyword><keyword><style  face="normal" font="default" size="100%">47D09</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/26/2/1.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">13</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, we consider a non-instantaneous impulsive system represented by the second order nonlinear differential equations in a Banach space. We use the strongly continuous cosine family of linear operators along with Schauder and Banach fixed point theorems to study the existence and uniqueness of the periodic solutions of the non-instantaneous impulsive system. Moreover, we construct a Poincar´e operator, which is a composition of the maps and we apply the techniques of a priori estimate for this operator. Finally, we give an example to illustrate the application of these obtained abstract results.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">2</style></issue><section><style face="normal" font="default" size="100%">197</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">LINA MA</style></author><author><style face="normal" font="default" size="100%">JINGXIAO ZHANG</style></author><author><style face="normal" font="default" size="100%">D. KANNAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">PRICING AN INSURANCE PRODUCT THAT INTEGRATES REVERSE MORTGAGE WITH LONG-TERM CARE INSURANCE</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/26/1/2.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">25</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We derive in this article the pricing formula for an insurance product that integrates reverse mortgage with long term care. This pricing is based on the principle of balance between the mean gain and mean payment. We compute the expected gain and the expected payment respectively under the continuous and discrete framework. Here, we assume that the dynamics of the housing price is driven by the Black-Scholes model and the interest rate is driven by the Ornstein-Uhlenbeck process. With these assumptions, we present closed-form formulas for the growing perpetuity annuity, the state annuity, and the constant annuity. Furthermore, we discuss the monotonicity property of the annuities, lump sum, and annuity payment factors with respect to the parameters of housing price, interest rate model, and the age of the insured. We present the numerical results for the lump sum, the annuity, and the annuity payment factors, and analyze the sensitivity with respect to the above parameters. We also show that the mean return of housing price has the dominating influence on the lump sum and annuity&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><section><style face="normal" font="default" size="100%">11</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">NESLIHAN  PELEN</style></author><author><style face="normal" font="default" size="100%">AYSE  GUVENILIR</style></author><author><style face="normal" font="default" size="100%">BILLUR KAYMAKÇALAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">SOME RESULTS ON PREDATOR-PREY DYNAMIC SYSTEMS WITH BEDDINGTON-DEANGELIS TYPE FUNCTIONAL RESPONSE ON TIME SCALE CALCULUS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/26/1/10.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">15</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We consider two dimensional predator-prey system with Beddington-DeAngelis type functional response on time scales. For this special case, we try to find under which conditions the system is permanent and globally attractive. This study gives beneficial results for continuous and discrete cases and also for solving open problems related to the dynamical properties of the systems which include the species that have unusual life cycle.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><section><style face="normal" font="default" size="100%">167</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">MARAT AKHMET</style></author><author><style face="normal" font="default" size="100%">AYSEGUL KIVILCIM</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">VERTICAL AND HORIZONTAL GRAZING</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34A37</style></keyword><keyword><style  face="normal" font="default" size="100%">34C25</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/26/1/7.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">15</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Grazing solutions of non-autonomous system with variable moments of impulses are examined. Appropriate denitions for vertial and horizontal grazing in non-autonomous systems are given and interpreted geometrially. The linearization for the periodi solutions whih have vertial or horizontal grazing is obtained. Examples are presented to demonstrate the pratiality of our results and they are visualized by the simulations.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><section><style face="normal" font="default" size="100%">131</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">MACIEJ KOZARYN</style></author><author><style face="normal" font="default" size="100%">MARIUSZ MICHTA</style></author><author><style face="normal" font="default" size="100%">KAMIL Ł. ŚWIĄTEK</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">STOCHASTIC INCLUSIONS DRIVEN BY TWO-PARAMETER MARTINGALES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">Random Field</style></keyword><keyword><style  face="normal" font="default" size="100%">Set-valued Stochastic Integral Equation</style></keyword><keyword><style  face="normal" font="default" size="100%">Stochastic Inclusion</style></keyword><keyword><style  face="normal" font="default" size="100%">Two-parameter martingale</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2016</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2016</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://www.acadsol.eu/dsa/articles/25/9.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">25</style></volume><pages><style face="normal" font="default" size="100%">30</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;The aim of the paper is the analysis of existence and properties of solutions to stochastic integral inclusions driven by two-parameter martingales. In our investigations we apply set-valued stochastic integral equations and we establish their connections with stochastic integral inclusions. Finally, we show how some particular two-parameter stochastic models are related to stochastic inclusions.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">123</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">BEHZAD DJAFARI ROUHANI</style></author><author><style face="normal" font="default" size="100%">HADI KHATIBZADEH</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ASYMPTOTIC BEHAVIOR FOR A GENERAL CLASS OF HOMOGENEOUS SECOND ORDER EVOLUTION EQUATIONS IN A HILBERT SPACE</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">39A23</style></keyword><keyword><style  face="normal" font="default" size="100%">47H05</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2015</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2015</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/24/01-dsa-01-16.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">24</style></volume><pages><style face="normal" font="default" size="100%">15</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We study the asymptotic behavior of solutions to the following general homogeneous second order evolution equation, with suitable assumptions on $p(t)$ and $r(t)$,&lt;/p&gt;

&lt;p&gt;$$ \left\{\begin{array}{ll} p(t)u^{\prime\prime}(t) + r(t)u^{\prime}(t) \in Au(t) &amp;amp; \text{a.e. on}\ R^+,\\ u(0) = u_0, &amp;amp; \sup_{t\geq 0} |u(t)| &amp;lt; +\infty, \end{array} \right.$$&lt;/p&gt;

&lt;p&gt;where $A$ is a maximal monotone operator in a real Hilbert space, and present some applications. In the homogeneous case, our results extend those given in [7, 10, 12].&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">1</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">S. B. KHAN</style></author><author><style face="normal" font="default" size="100%">N. U. AHMED</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">AN ATTEMPT TOWARDS DYNAMIC MODELING OF THE EARTH’S CLIMATE SYSTEM</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">35K51</style></keyword><keyword><style  face="normal" font="default" size="100%">35K55</style></keyword><keyword><style  face="normal" font="default" size="100%">76N99</style></keyword><keyword><style  face="normal" font="default" size="100%">93C20</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2015</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2015</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/24/12-dsa-155-168.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">24</style></volume><pages><style face="normal" font="default" size="100%">14</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper we attempt to develop a broader dynamic (mathematical) model for the climate system of the planet earth. This is based on two major components namely the atmosphere around the planet and the oceans all subject to the solar radiation, lunar gravity and their impact on land, sea and the atmosphere. It is assumed that the atmosphere-ocean interaction is the fundamental source of the global climate variability. Based on this fact we develop a mathematical model that takes into account all the possible major interactions. This model is further extended to a stochastic dynamic system in order to include uncertainties in many of the natural forces. The authors believe that this model will allow for numerical evaluation of many physical variables of interest possibly leading to a better understanding of the climate variability of the earth as a whole.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">155</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ZHANG JINGXIAO</style></author><author><style face="normal" font="default" size="100%">CAO KAI</style></author><author><style face="normal" font="default" size="100%">D. KANNAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">OPTIMAL PROPORTIONAL REINSURANCE AND INVESTMENT IN JUMP DIFFUSION MARKETS WITH NO SHORT-SELLING AND NO BORROWING</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2015</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2015</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/24/13-dsa-169-186.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">24</style></volume><pages><style face="normal" font="default" size="100%">17</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;The optimal reinsurance and investment problem for insurance has attracted a lot of attention of researchers in the field of stochastic control for a long time. Along this line we discuss this problem in the case of jump diffusion markets when neither short-selling nor borrowing is allowed. Here, we specifically assume that the risk process of the insurance company is a diffusion process. The insurance company can transfer its risk by reinsurance and also invest its surplus in the financial market, where we model the price of the risky asset by a geometric L´evy process. To maximize the CARA (Constant Absolute Risk Aversion) utility of terminal wealth, the HJB equation with no short-selling constraint has been considered, and we obtain the closed form of the value function by a standard method. However, only a handful of people have discussed this problem under both constraints, (i.e. no short-selling and no borrowing). This is because the problem is much more general in this context, and becomes so complex that analytical solution could hardly be obtained. Therefore, we provide, under the no short-selling and no borrowing constraints, a numerical solution via Markov chain approximation, which proves to be effective and amenable.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">169</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ILKAY YASLAN KARACA</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ON POSITIVE SOLUTIONS FOR FOURTH-ORDER FOUR-POINT BOUNDARY VALUE PROBLEMS WITH ALTERNATING COEFFICIENT ON TIME SCALES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B15</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2015</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2015</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/24/25-DSA-313-326.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">24</style></volume><pages><style face="normal" font="default" size="100%">14</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, by using four functionals fixed point theorem and five functionals fixed point theorem, we study the existence of at least one positive solution and three positive solutions respectively of a fourth-order four-point boundary value problem with alternating coefficient on a time scale. Examples are also included to illustrate our results.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">313</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ILKAY YASLAN KARACA</style></author><author><style face="normal" font="default" size="100%">FATMA TOKMAK</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">EXISTENCE OF THREE POSITIVE SOLUTIONS FOR M-POINT TIME SCALE BOUNDARY VALUE PROBLEMS ON INFINITE INTERVALS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B10</style></keyword><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2011</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2011</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/20/24-DSA-778.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">20</style></volume><pages><style face="normal" font="default" size="100%">13</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, by using the Leggett-Williams fixed point theorem and Five Functionals fixed point theorem, we establish the existence of three positive solutions for m-point time scale boundary value problems on infinite intervals. As an application, we also give some examples to demonstrate our results.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">355</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">TAHER S. HASSAN</style></author><author><style face="normal" font="default" size="100%">QINGKAI KONG</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">INTERVAL CRITERIA FOR FORCED OSCILLATION OF DIFFERENTIAL EQUATIONS WITH p-LAPLACIAN, DAMPING, AND MIXED NONLINEARITIES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34C10</style></keyword><keyword><style  face="normal" font="default" size="100%">34C15</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2011</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2011</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/20/19-DSA-31-17.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">20</style></volume><pages><style face="normal" font="default" size="100%">15</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We consider forced second order differential equation with p-Laplacian and damping in the form of (r(t)φα0 (x ′ ))′ + p(t)φα0 (x ′ ) +X N j=0 qj (t)φαj (x) = e(t), where φα (u) := |u| α sgn u, αj &amp;gt; 0, j = 0, 1, 2, . . . , N, and r, p, qj , e ∈ C ([0, ∞), R) with r (t) &amp;gt; 0 on [0, ∞). Interval oscillation criteria of the El-Sayed type and the Kong type are obtained. These criteria are further extended to equations with deviating arguments. Our work generalizes, unifies, and improves many existing results in the literature.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">279</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">JINGXIAO ZHANG</style></author><author><style face="normal" font="default" size="100%">SHENG LIU</style></author><author><style face="normal" font="default" size="100%">D. KANNAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">OPTIMAL DIVIDEND AND REINSURANCE UNDER THRESHOLD STRATEGY</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">60H10</style></keyword><keyword><style  face="normal" font="default" size="100%">60H30</style></keyword><keyword><style  face="normal" font="default" size="100%">93E20</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2011</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2011</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/20/14-DSA-31-07.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">20</style></volume><pages><style face="normal" font="default" size="100%">12</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We consider the optimal dividend and reinsurance problems in this article, where the dividend strategy is the threshold strategy and the reinsurance is the proportional reinsurance. Despite the fact that the barrier strategy has its popularity in theoretical research, such a strategy has little practical acceptance as it will lead to the certainty of ultimate ruin. A modified version of the barrier strategy is the threshold strategy which assumes that dividends are paid at a rate smaller than the rate of premium income whenever the surplus is above some threshold level, and that no dividends are paid out whenever the surplus is below the threshold level. In this article, we consider two cases of the threshold strategy. One is the threshold strategy without barrier, and the other is the threshold strategy with barrier. The first case generalizes and corrects part of results in [16]. In the second case, we use the stochastic control theoretic techniques, to find the value function as well as the optimal investment-reinsurance policy in closed form.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">193</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">JINGXIAO ZHANG</style></author><author><style face="normal" font="default" size="100%">SHENG LIU</style></author><author><style face="normal" font="default" size="100%">D. KANNAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">OPTIMAL DIVIDEND PROBLEM WITH THE INFLUENCE OF DIVIDEND PAYOUTS ON INSURANCE BUSINESS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">60H10</style></keyword><keyword><style  face="normal" font="default" size="100%">60H30</style></keyword><keyword><style  face="normal" font="default" size="100%">93E20</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2011</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2011</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/20/34-DSA-31-21.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">20</style></volume><pages><style face="normal" font="default" size="100%">12</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;This article initiates the optimal dividend problem, from the view point of the managers of the insurance companies. where we incorporate the influence of dividend payouts on the insurance business. We begin with a mathematical characterization of the influence of dividend payouts, and then continue to find the optimal dividend policy that maximizes the expected utility of terminal wealth and minimizes the ruin probability. We study the problem in terms of the Levy process and derive the diffusion process case as a particular one.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">519</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">JINGXIAO ZHANG</style></author><author><style face="normal" font="default" size="100%">SHENG LIU</style></author><author><style face="normal" font="default" size="100%">D. KANNAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">OPTIMAL INVESTMENT AND PROPORTIONAL REINSURANCE UNDER NO SHORT-SELLING AND NO BORROWING</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">60H10</style></keyword><keyword><style  face="normal" font="default" size="100%">60H30</style></keyword><keyword><style  face="normal" font="default" size="100%">93E20</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2011</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2011</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/20/15-DSA-31-10.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">20</style></volume><pages><style face="normal" font="default" size="100%">18</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Insurance companies resort to investment and reinsurance, among other options, to manage their reseerves. This article addresses the problem of optimal investment and reinsurance when no short-selling and no borrowing allowed. More specifically, we assume that the risk process of the insurance company is a compound Poisson process perturbed by a standard Brownian motion and that the risk can be reduced through a proportional reinsurance. In addition, the surplus can be invested in the financial market such that the portfolio will consist, for simplicity, of one risky asset and one risk-free asset. Our goal is to find the optimal investment and reinsurance policy which can maximize the expected exponential utility of the terminal wealth. In the case of no short-selling, we find the closed form of value function as well as the optimal investment-reinsurance policy. In the case when neither short-selling nor borrowing allowed, the resulting HJB equation is difficult to solve analytically, and hence we provide a numerical solution through Markov chain approximation techniques&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">205</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">MUJEEB UR REHMAN</style></author><author><style face="normal" font="default" size="100%">RAHMAT ALI KHAN</style></author><author><style face="normal" font="default" size="100%">PAUL  W. ELOE</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">POSITIVE SOLUTIONS OF NONLOCAL BOUNDARY VALUE PROBLEM FOR HIGHER ORDER FRACTIONAL DIFFERENTIAL SYSTEM</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2011</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2011</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/20/12-DSA-30-11.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">20</style></volume><pages><style face="normal" font="default" size="100%">14</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, we study existence and multiplicity results for a coupled system of nonlinear nonlocal boundary value problems for higher order fractional differential equations of the type    cDα 0+u(t) = λa(t)f(u(t), v(t)), cD β 0+v(t) = µb(t)g(u(t), v(t)), u ′ (0) = u ′′(0) = u ′′′(0) = · · · = u (n−1)(0) = 0, u(1) = ξ1u(η1), v ′ (0) = v ′′(0) = v ′′′(0) = · · · = v (n−1)(0) = 0, v(1) = ξ2v(η2), where λ, µ &amp;gt; 0, n − 1 &amp;lt; α, β ≤ n for n ∈ N; ξi , ηi ∈ (0, 1) for i = 1, 2 and cDα 0+ is Caputo fractional derivative. We employ the Guo-Krasnosel’skii fixed point theorem to establish existence and multiplicity results for positive solutions. We derive explicit intervals for the parameters λ and µ for which the system possess the positive solutions or multiple positive solutions. Examples are included to show the applicability of the main results.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">169</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">P. KARTHIKEYAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">SOME RESULTS FOR BOUNDARY VALUE PROBLEM OF AN INTEGRO DIFFERENTIAL EQUATIONS WITH FRACTIONAL ORDER</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34K05;26A33</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2011</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2011</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/20/02-DSA-291.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">20</style></volume><pages><style face="normal" font="default" size="100%">8</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;This paper discusses boundary value problem for fractional integrodifferential equations. We establish existence results by using the applications of Krasnoselkii theorem. An example is discussed to illustrate the efficiency of the obtained results.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">17</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">C. RATTANAKUL</style></author><author><style face="normal" font="default" size="100%">Y. LENBURY</style></author><author><style face="normal" font="default" size="100%">J. KONGSON</style></author><author><style face="normal" font="default" size="100%">W. TRIAMPO</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">THE DYNAMICS OF A NONLINEAR MODEL OF SIGNAL TRANSDUCTION IN HUMAN UNDER IMPULSIVE DEPRESSANT DRUG TREATMENT</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2010</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2010</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/19/46-DSA-30-06.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">19</style></volume><pages><style face="normal" font="default" size="100%">16</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;A mathematical model of the signal transduction process, involving hormone coupled receptors and an inhibiting enzyme, under impulsive depressant treatment, is proposed and analyzed. We show that there is a stable periodic solution, at the vanishing density of the ligand bound receptors on the cell membrane and plasmalemma, when the impulsive period is less than some critical value. The conditions for permanence of the system are then given. Finally, it is shown that as the impulsive period increases beyond a certain critical value, the emergence of stable positive periodic solution may be observed under appropriate conditions on the system parameters.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">651</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ROGER D. KIRBY</style></author><author><style face="normal" font="default" size="100%">A. G. LADDE</style></author><author><style face="normal" font="default" size="100%">G. S. LADDE</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ENERGY FUNCTION METHOD FOR SOLVING NONLINEAR DIFFERENTIAL EQUATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2010</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2010</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/19/24-DSA-29-09.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">19</style></volume><pages><style face="normal" font="default" size="100%">18</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;A very general conceptual algorithm for finding a solution process of a first order nonlinear differential equation is presented. The scope of this method is exhibited by showing the existing methods of solving nonlinear differential equations as special cases. Moreover, this approach extends for solving a larger class of nonlinear differential equations.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">335</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">NASEER AHMAD ASIF</style></author><author><style face="normal" font="default" size="100%">RAHMAT ALI KHAN</style></author><author><style face="normal" font="default" size="100%">JOHNNY HENDERSON</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">EXISTENCE OF POSITIVE SOLUTIONS TO A SYSTEM OF SINGULAR BOUNDARY VALUE PROBLEMS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B15</style></keyword><keyword><style  face="normal" font="default" size="100%">34B16</style></keyword><keyword><style  face="normal" font="default" size="100%">34b18</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2010</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2010</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/19/28-DSA-29-13.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">19</style></volume><pages><style face="normal" font="default" size="100%">10</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Existence results for positive solutions of a coupled system of nonlinear singular two point boundary value problems of the type&lt;/p&gt;

&lt;p&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; −x ′′(t) = p( t ) f(t, y( t ),&amp;nbsp;x′ (t) ),&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; t ∈ (0, 1),&lt;/p&gt;

&lt;p&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; −y ′′(t) = q( t ) g(t, x( t ),&amp;nbsp;y′ (t) ),&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;t ∈ (0, 1),&lt;/p&gt;

&lt;p&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; a&lt;sub&gt;1&lt;/sub&gt;x(0) − b&lt;sub&gt;1&lt;/sub&gt;x ′ (0) = x ′ (1) = 0,&lt;/p&gt;

&lt;p&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; a&lt;sub&gt;2&lt;/sub&gt;y(0) − b&lt;sub&gt;2&lt;/sub&gt;y ′ (0) = y ′ (1) = 0,&lt;/p&gt;

&lt;p&gt;are established. The nonlinearities f, g : [0, 1] × [0, ∞) × (0, ∞) → [0, ∞) are allowed to be singular at x ′ = 0 and y ′ = 0. The functions p, q ∈ C(0, 1) are positive on (0, 1) and the constants a&lt;sub&gt;i&lt;/sub&gt; , b&lt;sub&gt;i&lt;/sub&gt; (i = 1, 2) &amp;gt; 0. An example is included to show the applicability of our result.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">395</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ILKAY YASLAN KARACA</style></author><author><style face="normal" font="default" size="100%">OZLEM YILMAZ</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">FOURTH-ORDER M-POINT BOUNDARY VALUE PROBLEMS ON TIME SCALES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B10</style></keyword><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2010</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2010</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/19/19-DSA-257.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">19</style></volume><pages><style face="normal" font="default" size="100%">21</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Let T be a time scale with [a, b] ⊂ T. We establish criteria for existence of one or more than one positive solutions of the non-eigenvalue problem (0.1)    y △4 (t) − q(t)y ∆2 (σ(t)) = f(t, y(t)), t ∈ [a, b] ⊂ T, y(a) = Pm−2 i=1 aiy(ξi), y(σ 2 (b)) = Pm−2 i=1 biy(ξi), y ∆2 (a) = Pm−2 i=1 aiy ∆2 (ξi), y∆2 (σ 2 (b)) = Pm−2 i=1 biy ∆2 (ξi), where ξi ∈ (a, b), ai , bi ∈ [0, ∞) (for i ∈ {1, 2, . . . , m−2}) are given constants. Later, we consider the existence and multiplicity of positive solutions for the eigenvalue problem y △4 (t) − q(t)y ∆2 (σ(t)) = λf(t, y(t)) with the same boundary conditions. We shall also obtain criteria which lead to nonexistence of positive solutions. In both problems, we will use Krasnoselskii fixed point theorem.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">249</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">K. KROPIELNICKA</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">IMPLICIT DIFFERENCE METHODS FOR PARABOLIC FDE ON CYLINDRICAL DOMAINS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2010</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2010</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/19/39-DSA-269.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">19</style></volume><pages><style face="normal" font="default" size="100%">19</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Implicit difference schemes for quasilinear parabolic functional differential equations are presented. Ben- efits of implicit methods are pointed. The attention is focused here on cylindrical domains. Operators approximating mixed derivatives on irregular grids are introduced. A complete convergence analysis for methods is presented. Nonlinear estimates of the Perron type for given functions with respect to functional variables are used. Results obtained in the paper can be applied to differential integral problems and to equations with deviated variables. Numerical examples display the results of our investigations.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">557</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">QINGKAI KONG</style></author><author><style face="normal" font="default" size="100%">XIAOFEI WANG</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">NONLINEAR INITIAL VALUE PROBLEMS WITH p-LAPLACIAN</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34A12</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2010</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2010</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/19/03-DSA-03.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">19</style></volume><pages><style face="normal" font="default" size="100%">11</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We study the nonlinear initial value problem consisting of the equation − [ p(t) φ(y′ ) ]′ +&amp;nbsp;q(t) φ(y) = w(t) f(y) with φ(y) = |y|&lt;sup&gt;r−1&lt;/sup&gt;y for r &amp;gt; 0 and the initial conditions y(t&lt;sub&gt;0&lt;/sub&gt;) = y&lt;sub&gt;0&lt;/sub&gt;, (p&lt;sup&gt;1/r&amp;nbsp;&lt;/sup&gt;y′ ) (t&lt;sub&gt;0&lt;/sub&gt;) = z&lt;sub&gt;0&lt;/sub&gt;. By establishing nonlinear integral inequalities and applying a generalized energy function and a generalized Pr¨ufer transformation, we prove that the solution of this initial value problem exists on the whole domain and is unique. This paper provides a foundation for a forthcoming paper on the existence of nodal solutioins of second order nonlinear boundary value problems with p-Laplacian.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">33</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">V. JIMÉNEZ LÓPEZ</style></author><author><style face="normal" font="default" size="100%">J. KUPKA</style></author><author><style face="normal" font="default" size="100%">A. LINERO</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ON THE ω-LIMIT SETS OF PRODUCT MAPS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">37B99</style></keyword><keyword><style  face="normal" font="default" size="100%">37E05</style></keyword><keyword><style  face="normal" font="default" size="100%">37E99</style></keyword><keyword><style  face="normal" font="default" size="100%">54H20</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2010</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2010</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/19/47-DSA-182.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">19</style></volume><pages><style face="normal" font="default" size="100%">12</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Let ω(·)&amp;nbsp; denote the union of all ω-limit sets of a given map. As the main result of this paper we prove that, for given continuous interval maps f&lt;sub&gt;1&lt;/sub&gt;, . . . , f&lt;sub&gt;m&lt;/sub&gt;, the union of all ω-limit sets of the product map f&lt;sub&gt;1&lt;/sub&gt; × · · · × fm and the cartesian product of the sets ω(f&lt;sub&gt;1&lt;/sub&gt;), . . . , ω(f&lt;sub&gt;m&lt;/sub&gt;) coincide. This result enriches the theory of multidimensional permutation product maps, i.e., maps of the form F( x&lt;sub&gt;1&lt;/sub&gt;, . . . , x&lt;sub&gt;m&amp;nbsp;&lt;/sub&gt;) = ( f&lt;sub&gt;σ(1) &lt;/sub&gt;(x&lt;sub&gt;σ(1)&lt;/sub&gt;), . . . , f&lt;sub&gt;σ(m)&lt;/sub&gt;(x&lt;sub&gt;σ(m)&lt;/sub&gt;) ), where σ is a permutation of the set of indices {1, . . . , m}. For any such map F, we prove that the set ω(F) is closed and we also show that ω(F) cannot be a proper subset of the center of the map F. These results solve open questions mentioned, e.g., in [ F. Balibrea, J. S. Cánovas, A. Linero, New results on topological dynamics of antitriangular maps, Appl. Gen. Topol.].&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">667</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">JONG  PARK</style></author><author><style face="normal" font="default" size="100%">JUNG  KIM</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">EXISTENCE AND UNIFORM DECAY FOR A NONLINEAR VISCOELASTIC EQUATION WITH STRONG DAMPING AND NONLINEAR BOUNDARY MEMORY DAMPING TERM</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">35L90</style></keyword><keyword><style  face="normal" font="default" size="100%">74DXX</style></keyword><keyword><style  face="normal" font="default" size="100%">93D20</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2009</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2009</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/18/40-DSA-195.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">18</style></volume><pages><style face="normal" font="default" size="100%">15</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, we prove the existence of the solution to the nonlinear viscoelastic equation with strong damping and nonlinear boundary memory damping term. Moreover, we discuss the uniform decay of the solution&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">605</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">QINGKAI KONG</style></author><author><style face="normal" font="default" size="100%">QI-RU WANG</style></author><author><style face="normal" font="default" size="100%">ZHI-QIANG ZHU</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">KAMENEV-TYPE OSCILLATION CRITERIA FOR SECOND-ORDER MATRIX DYNAMIC EQUATIONS ON TIME SCALES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34C10</style></keyword><keyword><style  face="normal" font="default" size="100%">39A12</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2009</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2009</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/18/30-DSA-163.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">18</style></volume><pages><style face="normal" font="default" size="100%">17</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We consider the second order matrix valued dynamic equation ( P(t) X&lt;sup&gt;∆&lt;/sup&gt;(t) )&lt;sup&gt;∆&lt;/sup&gt; + Q(t) X( σ(t) ) = 0 on a time scale T, where P, Q ∈ C&lt;sub&gt;rd&lt;/sub&gt;(T, R&lt;sup&gt;n×n&lt;/sup&gt; ) with P(t) positive definite and Q(t) Hermitian on T. Kamenev type criteria and interval criteria are established. Our results cover those for matrix differential equations and provide new oscillation criteria for matrix difference equations.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">423</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ADINA OPRISAN</style></author><author><style face="normal" font="default" size="100%">ANDRZEJ KORZENIOWSKI</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">LARGE DEVIATIONS FOR ERGODIC PROCESSES IN SPLIT SPACES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">60B10</style></keyword><keyword><style  face="normal" font="default" size="100%">60F10</style></keyword><keyword><style  face="normal" font="default" size="100%">60H10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2009</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2009</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/18/39-DSA-194.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">18</style></volume><pages><style face="normal" font="default" size="100%">15</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We study a family of stochastic additive functionals of Markov processes with locally independent increments switched by jump Markov processes in an asymptotic split phase space. Based on an average approximation, we obtain a large deviation result for this stochastic evolutionary system using a weak convergence approach. Examples, including compound Poisson processes, illustrate cases in which the rate function is calculated in an explicit form.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">589</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">BASAK KARPUZ</style></author><author><style face="normal" font="default" size="100%">ÖZKAN  ÖCALAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">OSCILLATION AND NONOSCILLATION OF FIRST-ORDER DYNAMIC EQUATIONS WITH POSITIVE AND NEGATIVE COEFFICIENTS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34C10</style></keyword><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2009</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2009</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/18/26-DSA-154.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">18</style></volume><pages><style face="normal" font="default" size="100%">12</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this article, we investigate oscillatory nature of all solutions of a class of delay dynamic equations including positive and negative coefficients. Also we give a nonoscillation criterion for this class of delay dynamic equations. While our results reduce to the well-known oscillation criteria for the particular cases of the time scale, they improve recent results on arbitrary time scales. Further, we give some illustrating examples as applications of our results&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">363</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ILKAY  KARACA</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ON POSITIVE SOLUTIONS FOR HIGHER-ORDER BOUNDARY VALUE PROBLEMS WITH IMPULSE</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B10</style></keyword><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2009</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2009</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/18/46-DSA-224.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">18</style></volume><pages><style face="normal" font="default" size="100%">14</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, we consider a higher-order boundary value problem with impulse. We study the existence of at least one positive solution of an eigenvalue problem. Later, we establish the criteria for the existence of at least two positive solutions of a non-eigenvalue problem. Examples are also included to illustrate our results.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">687</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ANNE KANDLER</style></author><author><style face="normal" font="default" size="100%">MATTHIAS RICHTER</style></author><author><style face="normal" font="default" size="100%">JÜRGEN VOM SCHEIDT</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">SECOND ORDER MOMENTS OF SOLUTIONS OF PARABOLIC INITIAL BOUNDARY VALUE PROBLEMS WITH ε-CORRELATED RANDOM PARAMETERS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">60G60</style></keyword><keyword><style  face="normal" font="default" size="100%">60H35</style></keyword><keyword><style  face="normal" font="default" size="100%">65N30</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2009</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2009</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/18/13-DSA-27-05.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">18</style></volume><pages><style face="normal" font="default" size="100%">18</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Due to the random character of input data of a great variety of technical and economical procedures it seems to be appropriate to model these procedures by stochastic initial boundary value problems (IBVP). This paper deals with IBVP for parabolic partial differential equations where a Neumann boundary condition is assumed to be a random field with a given probability distribution. We assume, that this random field possesses smooth paths and that it is homogeneous and short-range correlated with a small correlation length ε &amp;gt; 0. The main interest lies in the calculation of the moment functions of the solution of the considered problem, which depend on the chosen characteristics of the random influence. Based on the idea of an appropriate FEM discretisation we present several approximation procedures for the computation of the variance and correlation function of the discretised solution. Considering a numerical example the resulting variance functions of the introduced methods are compared with the results of a Monte Carlo simulation.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">143</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">RAHMAT  KHAN</style></author><author><style face="normal" font="default" size="100%">JUAN NIETO</style></author><author><style face="normal" font="default" size="100%">ANGELA TORRES</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">APPROXIMATION AND RAPID CONVERGENCE OF SOLUTIONS FOR PERIODIC NONLINEAR PROBLEMS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34A45</style></keyword><keyword><style  face="normal" font="default" size="100%">34C25</style></keyword><keyword><style  face="normal" font="default" size="100%">92C50</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2008</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2008</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/17/DSA-2007-121-138.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">17</style></volume><pages><style face="normal" font="default" size="100%">17</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We study existence and approximation of solutions of some second order nonlinear periodic boundary value problem of the type&lt;/p&gt;

&lt;p&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;&amp;nbsp;−x''(t) = f(t, x, x' ),&amp;nbsp; &amp;nbsp; &amp;nbsp;&amp;nbsp;t ∈ [0, T],&lt;/p&gt;

&lt;p&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;x(0) = x(T),&amp;nbsp; x'(0) = x'(T),&lt;/p&gt;

&lt;p&gt;in the presence of lower and upper solutions. We develop the upper and lower solutions method and the quasilinearization technique for the existence and approximation of solutions. We apply our theoretical results to a medical problem.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">121</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">SHIH-SEN CHANG</style></author><author><style face="normal" font="default" size="100%">YEOL-JE CHO</style></author><author><style face="normal" font="default" size="100%">JONG-KYU KIM</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">APPROXIMATION METHODS OF SOLUTIONS FOR EQUILIBRIUM PROBLEM IN HILBERT SPACES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">47H09</style></keyword><keyword><style  face="normal" font="default" size="100%">47H10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2008</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2008</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/17/DSA-2007-503-514.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">17</style></volume><pages><style face="normal" font="default" size="100%">11</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;The purpose of this paper is, by using viscosity approximation methods, to find a common element of the set of solutions of an equilibrium problem and the set of fixed point of a nonexpansive mappings in a Hilbert space and to prove, under suitable conditions, some strong convergence theorems for approximating a solution of the problem under consideration.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">503</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">HÜSEYIN  BEREKETOGLU</style></author><author><style face="normal" font="default" size="100%">FATMA KARAKOÇ</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ASYMPTOTIC CONSTANCY FOR IMPULSIVE DELAY DIFFERENTIAL EQUATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34K06</style></keyword><keyword><style  face="normal" font="default" size="100%">34K45</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2008</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2008</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/17/DSA-2007-071-084.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">17</style></volume><pages><style face="normal" font="default" size="100%">13</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Sufficient conditions for the asymptotic constancy of the solutions of impulsive delay differential system ( x 0 (t) = A(t)[x(t − σ) − x(t − τ )] + f(t), t ≥ t0, t 6= ti , ∆x(ti) = Bix(ti) + Di , i = 1, 2, . . . , are obtained. Moreover, as t → ∞, the limits of the solutions of the impulsive delay differential system with Bi = 0 are computed in terms of the initial function and a special matrix solution of the corresponding adjoint system.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">71</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">K. BALACHANDRAN</style></author><author><style face="normal" font="default" size="100%">J.-H. KIM</style></author><author><style face="normal" font="default" size="100%">S.KARTHIKEYAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">COMPLETE CONTROLLABILITY OF STOCHASTIC INTEGRODIFFERENTIAL SYSTEMS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">93B05</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2008</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2008</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/17/DSA-2007-043-052.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">17</style></volume><pages><style face="normal" font="default" size="100%">10</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper sufficient conditions for the complete controllability of stochastic semilinear integrodifferential system in finite dimensional spaces are established. The results are obtained by using the Banach fixed point theorem. An example is provided to illustrate the technique.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">43</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ILKAY   KARACA</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">MULTIPLE POSITIVE SOLUTIONS FOR DYNAMIC m-POINT BOUNDARY VALUE PROBLEMS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B10</style></keyword><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2008</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2008</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/17/DSA-2007-025-042.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">17</style></volume><pages><style face="normal" font="default" size="100%">18</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, we consider a second order m-point boundary value problem for dynamic equations on time scales. First, we establish criteria for the existence of one or more than one positive solution of a non-eigenvalue problem. Second, we consider the existence and multiplicity of positive solutions for an eigenvalue problem. We shall also obtain criteria which lead to nonexistence of positive solutions. In both problems, we will use fixed point theorems for operators on a Banach space.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">25</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Ö. ÖCALAN</style></author><author><style face="normal" font="default" size="100%">M.K. YILDIZ</style></author><author><style face="normal" font="default" size="100%">B. KARPUZ</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ON THE OSCILLATION OF NONLINEAR NEUTRAL DIFFERENTIAL EQUATION WITH POSITIVE AND NEGATIVE COEFFICIENTS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34C10</style></keyword><keyword><style  face="normal" font="default" size="100%">34K40</style></keyword><keyword><style  face="normal" font="default" size="100%">34K99</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2008</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2008</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/17/DSA-2007-667-676.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">17</style></volume><pages><style face="normal" font="default" size="100%">9</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;This paper is focused on the following nonlinear neutral differential equation with positive and negative coefficients&lt;/p&gt;

&lt;p&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;[ x(t) − R(t) f( x(t − r)) ]′ + P(t) g(x(t − τ)) − Q(t )g( x(t − σ)) = 0,&lt;/p&gt;

&lt;p&gt;where R(t), P(t), Q(t) ∈ C ([t&lt;sub&gt;0&lt;/sub&gt;, ∞), R&lt;sup&gt;+&lt;/sup&gt;),&amp;nbsp; r &amp;gt; 0,&amp;nbsp; τ ≥ 0,&amp;nbsp; σ ≥ 0. For this equation, oscillation criteria are established.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">667</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">HARK-MAHN KIM</style></author><author><style face="normal" font="default" size="100%">SHEON-YOUNG KANG</style></author><author><style face="normal" font="default" size="100%">ICK-SOON CHANG</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ON THE STABILITY FOR CUBIC FUNCTIONAL EQUATION OF MIXED TYPE</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">39B52</style></keyword><keyword><style  face="normal" font="default" size="100%">39B72</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2008</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2008</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/17/DSA-2007-583-594.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">17</style></volume><pages><style face="normal" font="default" size="100%">12</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, we consider the general solution for a mixed type cubic functional equation lf( mX−1 i=1 xi + lxm) + lf( mX−1 i=1 xi − lxm) + 2 mX−1 i=1 f(lxi) = 2lf( mX−1 i=1 xi) + l 3 mX−1 i=1 [f(xi + xm) + f(xi − xm)], where l ≥ 2 and m ≥ 3 are any integers and investigate the Hyers-Ulam-Rassias stability of this equation.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">583</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">MICHAL KISIELEWICZ</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">WEAK COMPACTNESS OF WEAK SOLUTIONS TO BACKWARD STOCHASTIC DIFFERENTIAL INCLUSIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2008</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2008</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/17/DSA-2007-351-370.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">17</style></volume><pages><style face="normal" font="default" size="100%">20</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Weak compactness with respect to weak converegence in the Meyer-Zheng topology of sets of all weak solutions to backward stochastic differential inclusions is considered. Some existence theorems for backward stochastic differential inclusions are also given.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">351</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">MICHA  KISIELEWICZ</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">BACKWARD STOCHASTIC DIFFERENTIAL INCLUSIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">47H04</style></keyword><keyword><style  face="normal" font="default" size="100%">49J53</style></keyword><keyword><style  face="normal" font="default" size="100%">60H05</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2007</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/16/121-140-New-Kisielewicz-1.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">16</style></volume><pages><style face="normal" font="default" size="100%">19</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Existence of solutions to backward stochastic differential inclusions is considered. The paper contains the basic notions dealing with backward stochastic differential inclusions.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">121</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">BO ZHANG</style></author><author><style face="normal" font="default" size="100%">JING XU</style></author><author><style face="normal" font="default" size="100%">D. KANNAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A BACKWARDS STOCHASTIC DIFFERENTIAL EQUATION MODEL IN LIFE INSURANCE</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34F05</style></keyword><keyword><style  face="normal" font="default" size="100%">60H10</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2007</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/16/327-336-DSA-26-16-ZhangXuKannan.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">16</style></volume><pages><style face="normal" font="default" size="100%">9</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this article we obtain the ratio of risk investment and the optimal accumulated level of single premium endowment insurance in the case of dynamic investment strategies of life insurance company by BSDEs. It gives an illustration of traditional reserve valuation, and prudential rules.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">327</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">ERIC KAUFMANN</style></author><author><style face="normal" font="default" size="100%">YOUSSEF  RAFFOUL</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">STABILITY IN NEUTRAL NONLINEAR DYNAMIC EQUATIONS ON A TIME SCALE WITH FUNCTIONAL DELAY</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34K20</style></keyword><keyword><style  face="normal" font="default" size="100%">34K30</style></keyword><keyword><style  face="normal" font="default" size="100%">34K40</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2007</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/16/561-570-Kaufmann.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">16</style></volume><pages><style face="normal" font="default" size="100%">10</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Let T be a time scale that is unbounded above and below and such that 0 ∈ T. Let τ : T → T be such that τ (T) is a time scale. We use fixed point theorems to obtain stability results about the zero solution of the nonlinear neutral dynamic equation with functional delay&lt;/p&gt;

&lt;p&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; x&lt;sup&gt;∆&lt;/sup&gt;(t) = −a(t) x&lt;sup&gt;σ&lt;/sup&gt;(t) + c(t) x&lt;sup&gt;∆˜&lt;/sup&gt;( τ (t) ) + q( x(t), x( τ (t)) ) ,&amp;nbsp; &amp;nbsp;t ∈ T,&lt;/p&gt;

&lt;p&gt;where f&lt;sup&gt;∆&lt;/sup&gt; is the ∆-derivative on T and f&lt;sup&gt;∆˜&lt;/sup&gt; is the ∆-derivative on τ (T).&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">561</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">SVETOSLAV MARKOV</style></author><author><style face="normal" font="default" size="100%">NIKOLAY KYURKCHIEV</style></author><author><style face="normal" font="default" size="100%">ANTON ILIEV</style></author><author><style face="normal" font="default" size="100%">ASEN RAHNEV</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ON THE APPROXIMATION OF THE GENERALIZED CUT FUNCTION OF DEGREE p+1 BY SMOOTH HYPER–LOG–LOGISTIC FUNCTION</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">41A46</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">208</style></year><pub-dates><date><style  face="normal" font="default" size="100%">09/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/27/4/2.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">27</style></volume><pages><style face="normal" font="default" size="100%">14</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;We introduce a modification of the familiar cut function by replacing&amp;nbsp;the linear part in its definition by a polynomial of degree p + 1 obtaining thus a&amp;nbsp;sigmoid function called generalized cut function of degree p+1 (GCFP).We then study&amp;nbsp;the uniform approximation of the (GCFP) by smooth sigmoid functions such as the&amp;nbsp;hyper–log–logistic and the shifted hyper–log–logistic functions. The limiting case of&amp;nbsp;the interval-valued Heaviside step function is also discussed which imposes the use of&amp;nbsp;Hausdorff metric. Numerical examples are presented using CAS MATHEMATICA.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">4</style></issue><section><style face="normal" font="default" size="100%">715</style></section></record></records></xml>