<?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%">GEORGE E. CHATZARAKIS</style></author><author><style face="normal" font="default" size="100%">IRENA JADLOVSKA</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">DIFFERENCE EQUATIONS WITH SEVERAL NON-MONOTONE DEVIATING ARGUMENTS: ITERATIVE OSCILLATION TESTS</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><keyword><style  face="normal" font="default" size="100%">39A21</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%">03/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/27/2/5.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%">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;This paper is a study on the oscillatory behavior of the solutions of a&amp;nbsp;difference equation with several non-monotone deviating arguments and nonnegative&amp;nbsp;coefficients. New sufficient oscillation conditions involving lim sup are established&amp;nbsp;using an iterative method. The conditions obtained by this method achieve a marked&amp;nbsp;improvement on all known conditions, requiring at the same time far fewer iterations&amp;nbsp;to determine whether all solutions of the considered equations oscillate, than the&amp;nbsp;other known conditions. Examples, numerically solved in &lt;em&gt;MATLAB&lt;/em&gt;, are provided to&amp;nbsp;illustrate the results and the improvement achieved.&lt;br /&gt;
&amp;nbsp;&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">2</style></issue><section><style face="normal" font="default" size="100%">271</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%">MARTIN  BOHNER</style></author><author><style face="normal" font="default" size="100%">MAHMOUD  OSMAN</style></author><author><style face="normal" font="default" size="100%">SAMIR  SAKER</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">GENERAL HIGHER-ORDER DYNAMIC OPIAL INEQUALITIES WITH 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%">26D10</style></keyword><keyword><style  face="normal" font="default" size="100%">26D15</style></keyword><keyword><style  face="normal" font="default" size="100%">34A40</style></keyword><keyword><style  face="normal" font="default" size="100%">34N05</style></keyword><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword><keyword><style  face="normal" font="default" size="100%">39A13</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/26/1/4.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;In this paper, we present some new generalizations of dynamic Opial-type inequalities of higher order on time scales. The results contain as special cases many of the results currently given in literature. As an application, we apply these inequalities together with a Hardy-type inequality on time scales to establish some lower bounds of the distance between zeros of a solution and/or its derivatives for a fourth-order dynamic equation.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><section><style face="normal" font="default" size="100%">65</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%">VELI B. SHAKHMUROV</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">THE CAUCHY PROBLEM FOR GENERALIZED ABSTRACT BOUSSINESQ 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%">35Lxx</style></keyword><keyword><style  face="normal" font="default" size="100%">35Qxx</style></keyword><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword><keyword><style  face="normal" font="default" size="100%">43Axx</style></keyword><keyword><style  face="normal" font="default" size="100%">47Axx</style></keyword><keyword><style  face="normal" font="default" size="100%">47Hxx</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/25/8.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%">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, the existence and uniqueness of solution of the Cauchy problem for abstract Boussinesq equations is obtained. By applying this result, the Wentzell-Robin type mixed problem for Boussinesq equations and the Cauchy problem for finite or infinite systems of Boussinesq equations are studied.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">109</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%">ÖZKAN ÖZTÜRK</style></author><author><style face="normal" font="default" size="100%">ELVAN AKIN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">CLASSIFICATION OF NONOSCILLATORY SOLUTIONS OF NONLINEAR 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%">39A10</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/25/13.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%">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 the asymptotic behavior of nonoscillatory solutions of nonlinear dynamic equations on time scales. More precisely, all eventually monotone solutions of nonlinear dynamic equations can be divided into several disjoint subsets by means of necessary and sufficient integral conditions. Examples are given to illustrate some of our main results.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">219</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%">UMMAHAN AKCAN</style></author><author><style face="normal" font="default" size="100%">NUKET AYKUT HAMAL</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">EXISTENCE AND MONOTONE ITERATION OF CONCAVE POSITIVE SYMMETRIC SOLUTIONS FOR A THREE-POINT SECOND-ORDER BOUNDARY VALUE PROBLEMS WITH INTEGRAL 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%">34B10</style></keyword><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword><keyword><style  face="normal" font="default" size="100%">39B18</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/24/20-DSA-259-270.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%">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;In this article, we make use of the monotone iterative technique to verify the existence of concave symmetric positive solutions of a second-order three-point boundary value problem with integral boundary conditions. The interesting point here is that the nonlinear term f depends on the first-order derivative explicitly. An example which supports our result is also indicated.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">259</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%">ABDULKADIR DOGAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">THE EXISTENCE OF POSITIVE SOLUTIONS FOR A SEMIPOSITONE SECOND-ORDER m-POINT BOUNDARY VALUE PROBLEM</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%">34B15</style></keyword><keyword><style  face="normal" font="default" size="100%">34b18</style></keyword><keyword><style  face="normal" font="default" size="100%">39A10</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/24/33-DSA-419-428.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%">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 paper, we study the existence of positive solutions to boundary value problem&lt;/p&gt;

&lt;p&gt;$$ \left\{\begin{array}{ll} u^{\prime\prime} + \lambda f(t,u) = 0, &amp;amp; t \in (0, 1),\\ u(0) = \sum_{i=1}^{m-2}\alpha_i u(\xi_i), &amp;amp; u^{\prime}(1) = \sum_{i=1}^{m-2}\beta_i u^{\prime}(\xi_i), \end{array} \right. $$&lt;/p&gt;

&lt;p&gt;where $\xi_i \in&amp;nbsp;(0, 1)$, $0 &amp;lt; \xi_1 &amp;lt; \xi_2 &amp;lt;\cdots&amp;nbsp;&amp;lt; \xi_{m−2} &amp;lt; 1$, $\alpha_i , \beta_i \in&amp;nbsp;[0, ∞)$, $λ$ is positive parameter. By using Krasnosel’skii’s fixed point theorem, we provide sufficient conditions for the existence of at least one positive solution to the above boundary value problem.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">419</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%">ABDULKADIR DOGAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ON THE EXISTENCE OF POSITIVE SOLUTIONS FOR THE ONE-DIMENSIONAL p-LAPLACIAN 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%">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><keyword><style  face="normal" font="default" size="100%">39A10</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/24/23-DSA-295-304.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%">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 paper, we study the following p-Laplacian boundary value problems on time scales ( (φp(u ∆(t)))∇ + a(t)f(t, u(t), u∆(t)) = 0, t ∈ [0, T ]T, u(0) − B0(u ∆(0)) = 0, u∆(T ) = 0, where φp(u) = |u| p−2u, for p &amp;gt; 1. We prove the existence of triple positive solutions for the onedimensional p-Laplacian boundary value problem by using the Leggett-Williams fixed point theorem. The interesting point in this paper is that the non-linear term f is involved with first-order derivative explicitly. An example is also given to illustrate the main result.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">295</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%">Martin J. Bohner</style></author><author><style face="normal" font="default" size="100%">RAMY R. MAHMOUD</style></author><author><style face="normal" font="default" size="100%">SAMIR H. SAKER</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">IMPROVEMENTS OF DYNAMIC OPIAL-TYPE INEQUALITIES AND 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%">26D15</style></keyword><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword><keyword><style  face="normal" font="default" size="100%">39A12</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/24/18-dsa-229-242.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%">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 present some new improvements of dynamic Opial-type inequalities of first and higher order on time scales. We employ the new inequalities to prove several results related to the spacing between consecutive zeros of a solution and/or a zero of its derivative of a second-order dynamic equation with a damping term. The main results are proved by making use of a recently introduced new technique for Opial dynamic inequalities, the time scales integration by parts formula, the time scales chain rule, the time scales Taylor formula, and classical as well as time scales versions of H¨older’s inequality.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">229</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%">YI LIU</style></author><author><style face="normal" font="default" size="100%">XIAOPING XUE</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">THE MOTSCH-TADMOR MODEL WITH MULTIPLICATIVE WHITE NOISES IN FLOCKS</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%">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/24/40-DSA-503-522.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%">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;We enlarge the range of critical exponent β of the communication rate for unconditional flocking in the model proposed by Motsch, S. and Tadmor, E. [J. Statist. Phys., 141 (2011), 923–947], and describe an asymmetric stochastic model which emphasizes the asymmetric interaction between agents and employs the multiplicative white noise for the stochastic forces acting on ith-agent. For the case of asymmetric communication rate, we present sufficient conditions to guarantee the strong stochastic flocking to occur and show the almost sure exponential convergence toward constant equilibrium state through the control of the parameters and initial data. Our results are illustrated through the numerical simulations.&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%">ZHIGANG ZHANG</style></author><author><style face="normal" font="default" size="100%">XINZHI LIU</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">RAZUMIKHIN-TYPE STABILITY THEOREMS FOR IMPULSIVE DISCRETE SYSTEMS WITH TIME 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%">39A10</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/24/04-dsa-51-66.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%">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;This paper studies impulsive discrete systems with time delay. Several criteria on uniform stability and uniform asymptotic stability are established by utilizing the Razumikhin technique. Both linear and nonlinear impulsive discrete systems with time delay are investigated. These stability criteria show that impulses can be used to stabilize a unstable system. Some numerical examples are presented to illustrate the stability criteria.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">51</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%">XINQUAN ZHAO</style></author><author><style face="normal" font="default" size="100%">XINZHI LIU</style></author><author><style face="normal" font="default" size="100%">ZHIGANG ZHANG</style></author><author><style face="normal" font="default" size="100%">XIAOXIN LIAO</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">BOUNDEDNESS AND DISSIPATION FOR DISCRETE-TIME DYNAMIC 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%">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/20/05-DSA-30-14.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;This paper studies boundedness and dissipation of solutions of a class of discretetime dynamic systems. By the method of Lyapunov functions, some necessary and sufficient criteria on boundedness, equi-boundedness, uniform boundedness, and uniform dissipation are established. In addition, some sufficient criteria on dissipation, equi-dissipation and uniform dissipation are also obtained. Some examples are given to illustrate our results.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">55</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%">DA_BIN WANG</style></author><author><style face="normal" font="default" size="100%">WEN GUAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">NONLINEAR FIRST-ORDER SEMIPOSITONE PROBLEMS OF IMPULSIVE 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%">34B15</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/20/21-DSA-456.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%">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;By using the well-known Guo-Krasnoselskii fixed point theorem, in this paper, some results of one positive solution to a class of nonlinear first-order semipositone problems of impulsive dynamic equations on time scales are obtained. One example is given to illustrate the main results in this paper.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">307</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%">BAPURAO C. DHAGE</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">THEORETICAL APPROXIMATION METHODS FOR HYBRID 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%">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/20/30-DSA-31-08.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%">23</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, some existence theorems for the extremal solutions are proved for an initial value problem of nonlinear hybrid differential equations via constructive methods. The monotone iterative techniques for initial value problems of first order hybrid differential equations are developed and it is shown that the sequences of successive iterations defined in a certain way converge to the minimal and maximal solutions of the hybrid differential equations.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">455</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%">SAMUEL CASTILLO</style></author><author><style face="normal" font="default" size="100%">MANUEL PINTO</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ASYMPTOTIC BEHAVIOR OF FUNCTIONAL DYNAMIC EQUATIONS IN TIME SCALE</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/19/12-DSA-229.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%">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;It is considered a scalar linear functional dynamic equation in time scale with delayed argument of the form&lt;/p&gt;

&lt;p&gt;(0.1)&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; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;y&lt;sup&gt;∆&lt;/sup&gt;(t) = b(t) y( τ(t) ), t ∈ T ∩ [0, +∞]&lt;/p&gt;

&lt;p&gt;where T, the time scale, is a closed subset of R without upper bound for this case,&lt;sup&gt; ∆&lt;/sup&gt; is de Hilger’s derivate, which among other things, unifies difference operator for sequences and the derivate. The functions b, τ : T → C, τ &amp;gt; 0, are “locally integrable” and satisfy integral smallness conditions in a sense to be defined later. Asymptotic formulas of solutions of equation (0.1) are given. They unify and extend asymptotic formulas of difference and differential equations.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">165</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%">DA-BIN WANG</style></author><author><style face="normal" font="default" size="100%">XIA-YI WANG</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">EXISTENCE OF POSITIVE SOLUTIONS FOR NONLINEAR FIRST-ORDER IMPULSIVE 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%">34B15</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/19/35-DSA-241.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;By using the classical fixed point index theorem for compact maps and the Leggett-Williams fixed point theorem respectively, in this paper, some results of single and multiple positive solutions to a class of nonlinear first-order periodic boundary value problems of impulsive dynamic equations on time scales are obtained. Two examples are given to illustrate the main results in this paper.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">515</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%">WENJUN LIU</style></author><author><style face="normal" font="default" size="100%">QUÔC A NGÔ</style></author><author><style face="normal" font="default" size="100%">WENBING CHEN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ON NEW OSTROWSKI TYPE INEQUALITIES FOR DOUBLE INTEGRALS 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%">26D15</style></keyword><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword><keyword><style  face="normal" font="default" size="100%">39A12</style></keyword><keyword><style  face="normal" font="default" size="100%">39A13</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/19/14-DSA-237.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;A new Ostrowski type inequality for double integrals on time scales via ∆∆-integral is derived which unify corresponding continuous and discrete versions. Analogous results for ∇∇-, ∆∇- and ∇∆-integrals are also discussed.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">189</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%">CAI-XUN WANG</style></author><author><style face="normal" font="default" size="100%">HONG-RUI SUN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">POSITIVE SOLUTIONS FOR A CLASS OF SINGULAR THIRD-ORDER THREE-POINT NONHOMOGENEOUS BOUNDARY VALUE PROBLEM</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%">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/19/17-DSA-244.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;In this paper we establish the existence or nonexistence of positive solutions for singular third-order three-point nonhomogeneous boundary value problem. First, we give a new form of the solution, and then, some useful properties of the Green’s function are obtained by a new method. Finally, we employ a cone theoretic fixed-point index theorem to establish our results.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">225</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%">BAPURAO  DHAGE</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">APPLICABLE FIXED POINT THEORY IN FUNCTIONAL DIFFERENTIAL EQUATIONS ON UNBOUNDED 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%">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/18/47-DSA-227.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%">24</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 discuss the applications of some fixed point theorems to various types of functional differential equations for proving the existence as well as global attractivity and ultimate positivity of solutions on unbounded intervals under some usual natural conditions. Our hypotheses and claims have also been explained with the help of some natural realizations.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">701</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%">JOSEF DIBLIK</style></author><author><style face="normal" font="default" size="100%">IRENA HLAVICKOVA</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">COMBINATION OF LIAPUNOV AND RETRACT METHODS IN THE INVESTIGATION OF THE ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF SYSTEMS OF DISCRETE 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%">39A10</style></keyword><keyword><style  face="normal" font="default" size="100%">39A11</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/18/35-DSA-183.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%">31</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 contribution is devoted to a discussion of the asymptotic behavior of solutions of systems of first order nonlinear difference equations. We show that under appropriate conditions there exists at least one solution of the system considered the graph of which stays in a prescribed domain. The domains we work with are the so called polyfacial sets. In literature, retract and Liapunov type approaches are known as excellent asymptotic analysis tools. We present a method which connects both these techniques. Thanks to this, the achieved result can be applied to a substantially wider range of equations. The main result is applied to study a linear system of difference equations as well as to investigate a nonlinear system similar to the discrete scalar equation of Bernoulli’s type. Results are illustrated by detailed examples.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">507</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%">BIYING WANG</style></author><author><style face="normal" font="default" size="100%">ZHITING XU</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">OSCILLATION OF SECOND ORDER NEUTRAL EMDEN-FOWLER DELAY DYNAMIC EQUATIONS 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%">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/18/31-DSA-165.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;By means of generalized Riccati transformation and averaging technique, we establish some oscillation criteria for the second-order neutral Emden-Fowler delay dynamic equation of mixed 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; ( r(t)x&lt;sup&gt;∆&lt;/sup&gt;(t) )&lt;sup&gt;∆ &lt;/sup&gt;+ q&lt;sub&gt;1&lt;/sub&gt;(t) |y( δ(t) )|&lt;sup&gt;α−1&lt;/sup&gt; y( δ(t) ) + q&lt;sub&gt;2&lt;/sub&gt;(t) |y( δ(t) )|&lt;sup&gt;β−1&lt;/sup&gt; y( δ(t) ) = 0,&lt;/p&gt;

&lt;p&gt;on a time scale T. Our results as a special case when T = R improve some well known oscillation criteria for second order neutral Emden-Fowler delay differential equation of mixed type, and when T = N, T = hN, and T = q&lt;sup&gt;No&lt;/sup&gt; , i.e., for neutral delay difference equations, neutral delay difference equations with constant step size, and q-neutral difference equations with variable step size. The results obtained here are essentially new and can be applied to different types of time scales. Some applications and examples are considered to illustrate the main results.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">441</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%">YOU-HUI SU</style></author><author><style face="normal" font="default" size="100%">WAN-TONG LI</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">PERIODIC SOLUTION FOR NON-AUTONOMOUS SECOND ORDER HAMILTONIAN SYSTEMS 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%">34C25</style></keyword><keyword><style  face="normal" font="default" size="100%">37J45</style></keyword><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword><keyword><style  face="normal" font="default" size="100%">39A11</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/18/41-DSA-207.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%">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;We consider the following non-autonomous second order Hamiltonian system on time scales T of the form    u ∆∆(ρ(t)) = ▽H(t, u(t)) ∆-a.e. t ∈ [0, T ]T, u(0) − u(T ) = u ∆(ρ(0)) − u ∆(ρ(T )) = 0. As is well known, it is very difficult to use the Hilger’s integral to consider the existence of periodic solutions of some second order Hamiltonian systems on time scales since it is only concerned with antiderivatives. Therefore, in this paper, we use a new integral on time scales T defined by Rynne (J. Math. Anal. Appl. 328 (2007) 1217–1236), and establish a new existence result for periodic solutions in H1 T (T, R n) space of the above-mentioned second order Hamiltonian system on time scales T by applying variational methods and critical theory. As an application, an example is given to illustrate the result.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">621</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%">John R. Graef</style></author><author><style face="normal" font="default" size="100%">TOUFIK MOUSSAOUI</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">POSITIVE SOLUTIONS FOR DISCRETE 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%">34B16</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/18/21-DSA-28-10.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%">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;Existence results for positive solutions are established for a discrete Dirichlet boundary value problem. Various fixed point techniques including the Guo-Krasnosels’kii theorem and Schauder’s fixed point theorem are used. Examples illustrating the results are included.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">265</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%">RUYUN MA</style></author><author><style face="normal" font="default" size="100%">DONAL O’REGAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ASYMPTOTIC NONUNIFORM NONRESONANCE CONDITIONS FOR A NONLINEAR DISCRETE BOUNDARY VALUE PROBLEM</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-2007-271-282.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;Let T := {a+1, . . . , b+1}. We study the solvability of nonlinear discrete two-point boundary value problem ( ∆2u(t − 1) + g(t, u(t)) = h(t), t ∈ T, u(a) = u(b + 2) = 0 where h : T → R, g : T × R → R satisfies α(t) ≤ lim inf |x|→∞ x −1 g(t, x) ≤ lim sup |x|→∞ x −1 g(t, x) ≤ β(t) uniformly on T, and α and β satisfy some nonresonance conditions of nonuniform type with respect to two consecutive eigenvalues of the associated linear problem. The proof is based on the LeraySchauder continuation theorem.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">271</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%">A. M. SAMOILENKO</style></author><author><style face="normal" font="default" size="100%">N. I. MAHMUDOV</style></author><author><style face="normal" font="default" size="100%">A. N. STANZHITSKII</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">EXISTENCE, UNIQUENESS, AND CONTROLLABILITY RESULTS FOR NEUTRAL FSDES 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%">39A10</style></keyword><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-2007-053-070.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;We establish results concerning the global existence, uniqueness, and controllability of mild solutions for a neutral functional stochastic differential equations with variable delay in a real separable Hilbert space. The results are obtained by imposing a so-called Carathe´odory condition on the nonlinearities, which is weaker than the classical Lipschitz condition. Examples illustrating the applicability of the general theory are also provided.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">53</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%">HAO HUANG</style></author><author><style face="normal" font="default" size="100%">QI-RU WANG</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">OSCILLATION OF SECOND-ORDER NONLINEAR 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%">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-2007-551-570.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;By using the functions of the form H(t, s) and a generalized Riccati technique, we establish new Kamenev-type and interval oscillation criteria for second-order nonlinear dynamic equations on time scales of the form&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;( p(t)x&lt;sup&gt;∆&lt;/sup&gt;(t) )&lt;sup&gt;∆&lt;/sup&gt; + f( t, x(σ(t)) ) = 0.&lt;/p&gt;

&lt;p&gt;The obtained interval oscillation criteria can be applied to equations with forcing term. Two examples are included to show the significance of the results.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">551</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%">JIAN-PING SUN</style></author><author><style face="normal" font="default" size="100%">WAN-TONG LI</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">SOLUTIONS AND POSITIVE SOLUTIONS TO SEMIPOSITONE DIRICHLET BVPS 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><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-2007-303-312.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;In this paper, we are concerned with the following Dirichlet boundary value problem on a time scale T ( −u ∆∆(t) = g(t, u(t)), t ∈ [0, T]T, u(0) = 0 = u(σ 2 (T)), where g : [0, T]T×[−σ(T)σ 2 (T)M, +∞) → [−M, +∞) is continuous and M &amp;gt; 0 is a constant, which implies that this problem is semipositone. For an arbitrary positive integer n, some existence results for n solutions and/or positive solutions are established by using the well-known Guo-Krasnosel’skii fixed point theorem. Our conditions imposed on g are local. An example is also included to illustrate the importance of the results obtained.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">303</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%">YOU-WEI ZHANG</style></author><author><style face="normal" font="default" size="100%">HONG-RUI SUN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">THREE POSITIVE SOLUTIONS FOR A GENERALIZED STURM-LIOUVILLE MULTIPOINT BVP WITH DEPENDENCE ON THE FIRST ORDER DERIVATIVE</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%">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-2007-313-324.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 are concerned with the following generalized Sturm-Liouville multipoint boundary value problem u 00(t) + h (t) f (t, u (t), u 0 (t)) = 0, 0 &amp;lt; t &amp;lt; 1, au (0) − bu0 (0) = mX−2 i=1 aiu(ξi), cu (1) + du0 (1) = mX−2 i=1 biu(ξi), where 0 &amp;lt; ξ1 &amp;lt; · · · &amp;lt; ξm−2 &amp;lt; 1 (m ≥ 3), a, b, c, d ∈ [0, ∞), ai , bi ∈ (0, ∞) (i = 1, 2, . . . , m − 2) are constants satisfying some suitable conditions. Existence criteria for at least three positive solutions are established by using the fixed point theorem of Avery and Peterson. The interesting point is the nonlinear term f which is involved with the first order derivative explicitly.&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%">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%">NAZIM  MAHMUDOV</style></author><author><style face="normal" font="default" size="100%">MARK  MCKIBBEN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ON A CLASS OF BACKWARD MCKEAN-VLASOV STOCHASTIC EQUATIONS IN HILBERT SPACE: EXISTENCE AND CONVERGENCE PROPERTIES</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%">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/16/643-664-DSA-022.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%">22</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 investigation is devoted to the study of a class of abstract first-order backward McKean-Vlasov stochastic evolution equations in a Hilbert space. Results concerning the existence and uniqueness of solutions and the convergence of an approximating sequence of solutions (and corresponding probability measures) are established. Examples that illustrate the abstract theory are also provided.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">643</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%">JIAN-PING SUN</style></author><author><style face="normal" font="default" size="100%">WAN-TONG LI</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">EXISTENCE OF POSITIVE SOLUTIONS TO SEMIPOSITONE DIRICHLET BVPS 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><keyword><style  face="normal" font="default" size="100%">39A10</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/16/571-578-SunLi.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%">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;In this paper, we are concerned with the following semipositone Dirichlet boundary value problem on a time scale T ( −u ∆∆(t) = g(t, u(t)), t ∈ [0, T]T, u(0) = 0 = u(σ 2 (T)), where g : [0, T]T × [0, +∞) → [−M, +∞) is continuous and M &amp;gt; 0 is a constant. Some existence criteria for at least one positive solution are established by using well-known results from fixed point index theory.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">571</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.H. SAKER</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">OSCILLATION OF SECOND-ORDER DELAY AND NEUTRAL DELAY 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%">34A99</style></keyword><keyword><style  face="normal" font="default" size="100%">34C10</style></keyword><keyword><style  face="normal" font="default" size="100%">34K11</style></keyword><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword><keyword><style  face="normal" font="default" size="100%">39A11</style></keyword><keyword><style  face="normal" font="default" size="100%">39A99</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/16/345-360-DSA-26-18-Saker.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%">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 consider the second-order linear delay dynamic equation x ∆∆(t) + q(t)x(τ (t)) = 0, on a time scale T. We will study the properties of the solutions and establish some sufficient conditions for oscillations. In the special case when T = R and τ (t) = t, our results include some well-known results in the literature for differential equations. When, T = Z, T = hZ, for h &amp;gt; 0 and T = Tn = {tn : n ∈ N0} where tn} is the set of the harmonic numbers defined by t0 = 0, tn = Pn k=1 1 k for n ∈ N0 our results are essentially new. The results will be applied on second-order neutral delay dynamic equations in time scales to obtain some sufficient conditions for oscillations. An example is considered to illustrate the main results.&lt;/p&gt;
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