<?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%">RABIAA AOUAFI</style></author><author><style face="normal" font="default" size="100%">NACER ADJEROUD</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">THE EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR A MULTI-TERM NONLINEAR SEQUENTIAL FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS WITH TREE-POINT BOUNDARY CONDITIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Communications in Applied Analysis</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34A08</style></keyword><keyword><style  face="normal" font="default" size="100%">34B10</style></keyword><keyword><style  face="normal" font="default" size="100%">34B15</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/en/articles/22/3/9.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">22</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 study a new class of boundary value problems of multiterm nonlinear sequential fractional integro-differential equations with three-point nonlocal fractional boundary conditions. Some existence and uniqueness&lt;br /&gt;
results are obtained by using standard fixed point theorems. An example is&amp;nbsp;given to illustrate our results.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">3</style></issue><work-type><style face="normal" font="default" size="100%">scientific: mathematics</style></work-type><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%">SMITA PATI</style></author><author><style face="normal" font="default" size="100%">SESHADEV PADHI</style></author><author><style face="normal" font="default" size="100%">P.D.N. SRINIVASU</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">CONDITIONS FOR EXISTENCE OF POSITIVE SOLUTIONS OF FIRST ORDER BOUNDARY VALUE PROBLEMS WITH DELAY AND NONLINEAR NONLOCAL BOUNDARY CONDITIONS AND APPLICATION TO HEMATOPOIESIS</style></title><secondary-title><style face="normal" font="default" size="100%">Communications in Applied Analysis</style></secondary-title><alt-title><style face="normal" font="default" size="100%">CAA</style></alt-title><short-title><style face="normal" font="default" size="100%">Existence of Positive Solutions</style></short-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B08</style></keyword><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></keywords><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">01/2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.acadsol.eu/en/articles/21/1/4.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">21</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, &amp;nbsp;existence criteria for &amp;nbsp; positive solutions of the following nonlinear first order boundary value problem with delay and &amp;nbsp;nonlinear nonlocal boundary condition&lt;br /&gt;
&amp;nbsp;\begin{eqnarray*}&lt;br /&gt;
&amp;nbsp;x^{\prime}(t) &amp;amp; = &amp;amp; r(t)x(t) + p(t) \sum_{i=1}^{m} f_i(t,x(\alpha_{i}(t))), \,\,\, t \in [0,1],\\&lt;br /&gt;
&amp;nbsp;\lambda x(0) &amp;amp; = &amp;amp; x(1) + \sum_{j=1}^{n} \Lambda_j(\tau_j, x(\tau_j)),\,\,\, \tau_j \in [0,1],&lt;br /&gt;
&amp;nbsp;\end{eqnarray*}&lt;br /&gt;
&amp;nbsp;are established using &amp;nbsp;Leray-Schauder theorem and Leggett-Williams fixed point theorem. These results are employed to &amp;nbsp;provide a complete existence criteria for positive solutions of the following &amp;nbsp;boundary value problem associated with the well known Hematopoiesis &amp;nbsp;model%\vfill\mbox{}\newpage&lt;br /&gt;
&amp;nbsp;\begin{align}&lt;br /&gt;
&amp;nbsp;x^{\prime}(t) &amp;nbsp;= &amp;amp; r(t)x(t) + p(t)\frac{x^{n}(t-\alpha)}{1+x^{m}(t-\alpha)}, \,\,\, t \in [0,1], \nonumber\\&lt;br /&gt;
&amp;nbsp; \lambda x(0) &amp;nbsp; = &amp;amp; &amp;nbsp;x(1) &amp;nbsp;+ &amp;nbsp;\Lambda(\tau,x(\tau)),\,\,\, \tau \in [0,1] \nonumber&lt;br /&gt;
&amp;nbsp;\end{align}&lt;br /&gt;
&amp;nbsp;where $m$ and $n$ are nonnegative parameters.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><work-type><style face="normal" font="default" size="100%">scientific: mathematics</style></work-type><section><style face="normal" font="default" size="100%">39</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%">MOHAMMED DERHAB</style></author><author><style face="normal" font="default" size="100%">HAYAT MEKNI</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">EXISTENCE OF MINIMAL AND MAXIMAL SOLUTIONS FOR A QUASILINEAR DIFFERENTIAL EQUATION WITH NONLOCAL BOUNDARY CONDITION ON THE HALF-LINE</style></title><secondary-title><style face="normal" font="default" size="100%">Communications in Applied Analysis</style></secondary-title><short-title><style face="normal" font="default" size="100%">EXISTENCE OF MINIMAL AND MAXIMAL SOLUTIONS</style></short-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></keywords><dates><year><style  face="normal" font="default" size="100%">2016</style></year><pub-dates><date><style  face="normal" font="default" size="100%">06/2016</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.acadsol.eu/en/articles/20/2/3.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 class=&quot;rtejustify&quot;&gt;This work is concerned with the construction of minimal and maximal solutions for a second order quasilinear differential equation on the half-line with nonlocal boundary condition and without condition at infinity, where the nonlinearity is a continuous function depending on the first derivative of the unknown function. We also give an example to illustrate our results.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">2</style></issue><work-type><style face="normal" font="default" size="100%">scientific: mathematics</style></work-type><section><style face="normal" font="default" size="100%">209</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%">JOHNNY HENDERSON</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">EXISTENCE OF LOCAL SOLUTIONS FOR BOUNDARY VALUE PROBLEMS WITH INTEGRAL CONDITIONS</style></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></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%">http://www.acadsol.eu/en/articles/19/1/8.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%">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;Conditions are given for the existence of local solutions of the nth order ordinary differential equation, ${ y^{(n)}+f(x, y, y′ , . . . , y^{(n−1)}) = 0 }$, satisfying the respective Dirichlet and nonlocal integral boundary conditions, ${ y^{(i−1)}(a) = A_i ,\&amp;nbsp; i = 1, . . . , n − 1,}$ and ${\int^b_a y(x) dx = A_n }$.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><section><style face="normal" font="default" size="100%">103</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 R. Kaufmann</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">EXISTENCE OF POSITIVE SOLUTIONS TO A SECOND-ORDER DIFFERENTIAL EQUATION AT RESONANCE</style></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></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%">http://www.acadsol.eu/en/articles/19/4/3.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%">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;We establish sufficient conditions for the existence of positive solutions to the multipoint boundary value $${ −u ′′ = f(t, u(t)), \ \ \ \ t ∈ (0, 1), \\ \ \ \&amp;nbsp; u(0) = u(1), \\ \ \ u ′ (0) = u ′ (η). }$$ Since the associated homogeneous boundary value problem is not invertible the problem is said to be at resonance. The main tool employed is a variant of a fixed point index theorem due to Cremins for A-proper semilinear operators defined on cones.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">4</style></issue><section><style face="normal" font="default" size="100%">505</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%">RODICA LUCA</style></author><author><style face="normal" font="default" size="100%">ALEXANDRU TUDORACHE</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">EXISTENCE OF POSITIVE SOLUTIONS TO A SYSTEM OF HIGHER-ORDER SEMIPOSITONE INTEGRAL BOUNDARY VALUE PROBLEMS</style></title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B10</style></keyword><keyword><style  face="normal" font="default" size="100%">34B18</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%">http://www.acadsol.eu/en/articles/19/4/10.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;We investigate the existence of positive solutions for a system of nonlinear higherorder ordinary differential equations with sign-changing nonlinearities, subject to integral boundary conditions.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">4</style></issue><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%">QINGKAI KONG</style></author><author><style face="normal" font="default" size="100%">THOMAS E. ST. GEORGE</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">MATCHING METHOD FOR NODAL SOLUTIONS OF BOUNDARY VALUE PROBLEMS WITH INTEGRAL BOUNDARY CONDITIONS</style></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></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%">http://www.acadsol.eu/en/articles/19/1/10.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;In this paper, we study the nonlinear boundary value problem consisting of the equation ${ y′′+ \int^{b}_{a} &amp;nbsp;w(t, τ)f(y, τ) \ dζ(τ) = 0 }$ on&amp;nbsp; [a, b] and a double Riemann-Stieltjes integral boundary condition. We establish the existence of various nodal solutions of this problem by matching the solutions of two boundary value problems, each of which involves one separated boundary condition and open Riemann-Stieltjes integral boundary condition, at some point in (a, b). We also obtain the conditions for nonexistence of nodal solutions of this boundary value problem.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><section><style face="normal" font="default" size="100%">129</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%">Abdelkader Boucherif</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">POSITIVE SOLUTIONS OF NONLOCAL MULTIPOINT BOUNDARY VALUE PROBLEMS</style></title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B10</style></keyword><keyword><style  face="normal" font="default" size="100%">34B18</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%">http://www.acadsol.eu/en/articles/19/3/8.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 class=&quot;rtejustify&quot;&gt;We investigate the existence of positive solutions of nonlocal multipoint boundary value problems for second order nonlinear differential equations. The nonlinearity depends on the derivative of the unknown function, and is allowed to change sign infinitely many times. We rely the method of lower and upper solutions to prove our main result. In fact, using the same technique, we obtain a multiplicity result without extra assumptions.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">3</style></issue><section><style face="normal" font="default" size="100%">427</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%">XUEYAN LIU</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">THE SOLUTION MATCHING BY LIAPUNOV THEORY OF BVPS WITH ODD GAPS IN BOUNDARY CONDITIONS FOR nTH ORDER DIFFERENTIAL EQUATIONS</style></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></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%">http://www.acadsol.eu/en/articles/19/4/9.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 class=&quot;rtejustify&quot;&gt;We are concerned with the existence and uniqueness of solutions to boundary value problems on an interval [a, c] for the nth order ordinary differential equation ${ y^{(n)} = f(x, y, y′ , . . . , y^{(n−1)}), }$ for ${n ≥ 3,}$ by matching solutions on [a, b] with solutions on [b, c] to extend the interval of existence for solutions. In this paper, we consider a general case where the gap in boundary conditions at b is odd. Different from the literature, we use Liapunov theory to deal with the case&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">4</style></issue><section><style face="normal" font="default" size="100%">579</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%">FELIZ MINHÓS</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">EXISTENCE OF EXTREMAL SOLUTIONS FOR SOME FOURTH ORDER FUNCTIONAL BVPS</style></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%">34K10</style></keyword><keyword><style  face="normal" font="default" size="100%">34K12</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%">http://www.acadsol.eu/en/articles/15/4/10.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">15</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 work we present sufficient conditions for the existence of extremal solutions for the fourth order functional problem composed by the equation&amp;nbsp;&lt;/p&gt;

&lt;p&gt;− &lt;em&gt;(${\phi}$(u′′′(x) ))′= f (x, u′′(x), u′′′(x), u,u′,u′′ ) ,&lt;/em&gt;&lt;/p&gt;

&lt;p class=&quot;rtejustify&quot;&gt;for&lt;em&gt; a.a.x&lt;/em&gt; ∈ [0, 1] , where &lt;em&gt;${\phi}$&lt;/em&gt; is an increasing homeomorphism, ${\text { I }}$:= [0, 1], and ${\ f:I }$ ${\times }$ ${\mathbb{R}^2}$&amp;nbsp;${\times }$ ${\ ( \ C\ ( I\ ) )^3 \to&amp;nbsp;\mathbb{R} }$ is a L&lt;sup&gt;1&lt;/sup&gt; -Carathéodory function, and the boundary conditions&lt;/p&gt;

&lt;p&gt;&lt;em&gt;0 = L&lt;sub&gt;1&amp;nbsp;&lt;/sub&gt;( u(a), u,u′,u′′ )&lt;/em&gt;&lt;/p&gt;

&lt;p&gt;&lt;em&gt;0 = L&lt;sub&gt;2&lt;/sub&gt; ( u′(a), u,u′,u′′ ) &lt;/em&gt;&lt;/p&gt;

&lt;p&gt;&lt;em&gt;0 = L&lt;sub&gt;3&lt;/sub&gt; ( u′′(a), u′′(b), u′′′(a), u′′′(b), u,u′,u′′ )&lt;/em&gt;&lt;/p&gt;

&lt;p&gt;&lt;em&gt;0 = L&lt;sub&gt;4&lt;/sub&gt; ( u′′(a), u′′(b) )&lt;/em&gt;&lt;/p&gt;

&lt;p class=&quot;rtejustify&quot;&gt;where &lt;em&gt;L&lt;sub&gt;i&lt;/sub&gt;&lt;/em&gt; , i = 1, 2, 3, 4, are suitable functions with&lt;em&gt; L&lt;sub&gt;1&lt;/sub&gt;&lt;/em&gt; and &lt;em&gt;L&lt;sub&gt;2&lt;/sub&gt; &lt;/em&gt;not necessarily continuous, satisfying some monotonicity assumptions. The arguments make use of lower and upper solutions technique, a version of Bolzano’s theorem and existence of extremal fixed points for a suitable mapping.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">4</style></issue><section><style face="normal" font="default" size="100%">547</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%">FRANCOIS GENOUD</style></author><author><style face="normal" font="default" size="100%">BRYAN P. RYNNE</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">SOME RECENT RESULTS ON THE SPECTRUM OF MULTI-POINT EIGENVALUE PROBLEMS FOR THE p-LAPLACIAN</style></title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B08</style></keyword><keyword><style  face="normal" font="default" size="100%">34B10</style></keyword><keyword><style  face="normal" font="default" size="100%">34L05</style></keyword><keyword><style  face="normal" font="default" size="100%">47J15</style></keyword><keyword><style  face="normal" font="default" size="100%">47N20</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%">http://www.acadsol.eu/en/articles/15/4/1.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">15</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 describe some recent results regarding the spectral properties of &lt;em&gt;p&lt;/em&gt;-Laplacian problems subject to various forms of multi-point boundary conditions. In particular, we consider Dirichlet and Neumann-type boundary conditions, and mixtures of these conditions. We also consider certain types of nonlocal boundary conditions expressed in terms of Stieltjes integrals, which have been discussed recently and which generalize the previously considered multi-point conditions. It is shown that, under suitable assumptions, the structure of the spectrum and the properties of the eigenfunctions for these boundary value problems with nonlocal boundary conditions are very similar to those of the classical linear Sturm-Liouville problem with separated boundary conditions. Results on global bifurcation, non-resonance conditions and existence of nodal solutions for related nonlinear problems are also presented. In a final section we discuss the necessity of some of the hypotheses we impose, and outline some open problems.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">4</style></issue><section><style face="normal" font="default" size="100%">413</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%">BASHIR AHMAD</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">APPROXIMATION OF SOLUTIONS OF THE FORCED DUFFING EQUATION WITH m-POINT BOUNDARY CONDITIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Communications in Applied Analysis</style></secondary-title><short-title><style face="normal" font="default" size="100%">APPROXIMATION OF SOLUTIONS OF THE FORCED DUFFING EQUATION</style></short-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></keywords><dates><year><style  face="normal" font="default" size="100%">2009</style></year><pub-dates><date><style  face="normal" font="default" size="100%">01/2009</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.acadsol.eu/en/articles/13/1/2.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">13</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;div class=&quot;rtejustify&quot;&gt;In this paper, we discuss the existence and uniqueness of the solution of the forced Duffing equation with m-point boundary conditions. A monotone sequence of approximate solutions converging uniformly and quadratically to the unique solution of the problem is obtained by applying a generalized quasilinearization technique.&lt;/div&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><work-type><style face="normal" font="default" size="100%">scientific: mathematics</style></work-type><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%">MOUFFAK BENCHOHRA</style></author><author><style face="normal" font="default" size="100%">JOHNNY HENDERSON</style></author><author><style face="normal" font="default" size="100%">DJAMILA SEBA</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">MEASURE OF NONCOMPACTNESS AND FRACTIONAL DIFFERENTIAL EQUATIONS IN BANACH SPACES</style></title></titles><keywords><keyword><style  face="normal" font="default" size="100%">26A33</style></keyword><keyword><style  face="normal" font="default" size="100%">34B10</style></keyword><keyword><style  face="normal" font="default" size="100%">34G20</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%">http://www.acadsol.eu/en/articles/12/4/5.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">12</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, the existence of solutions for an initial value problem of a fractional differential equation is obtained by means of M¨onch’s fixed point theorem and the technique of measures of noncompactness.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">4</style></issue><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%">JOHN ALLISON</style></author><author><style face="normal" font="default" size="100%">NICKOLAI KOSMATOV</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">MULTI-POINT BOUNDARY VALUE PROBLEMS OF FRACTIONAL ORDER</style></title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34A12</style></keyword><keyword><style  face="normal" font="default" size="100%">34A34</style></keyword><keyword><style  face="normal" font="default" size="100%">34B10</style></keyword><keyword><style  face="normal" font="default" size="100%">45D05</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%">http://www.acadsol.eu/en/articles/12/4/8.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">12</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 study multi-point boundary value problems of fractional order with the Riemann-Liouville and Caputo fractional derivatives. The existence results are obtained using the Schauder fixed point theorem.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">4</style></issue><section><style face="normal" font="default" size="100%">451</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%">Gennaro Infante</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">NONLOCAL BOUNDARY VALUE PROBLEMS WITH TWO NONLINEAR BOUNDARY CONDITIONS</style></title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B10</style></keyword><keyword><style  face="normal" font="default" size="100%">34B18</style></keyword><keyword><style  face="normal" font="default" size="100%">47H10</style></keyword><keyword><style  face="normal" font="default" size="100%">47H30</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%">http://www.acadsol.eu/en/articles/12/3/4.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">12</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;We establish new results on the existence of positive solutions for some nonlocal boundary value problems subject to two nonlinear boundary conditions. Our approach relies on the classical fixed point index theory for compact maps.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">3</style></issue><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%">AI-LING SHI</style></author><author><style face="normal" font="default" size="100%">HAI-E ZHANG</style></author><author><style face="normal" font="default" size="100%">JIAN-PING SUN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">SINGULAR THIRD-ORDER m-POINT BOUNDARY VALUE PROBLEMS</style></title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B10</style></keyword><keyword><style  face="normal" font="default" size="100%">34B16</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%">http://www.acadsol.eu/en/articles/12/3/9.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">12</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 paper is concerned with the following third-order m-point boundary value problem $${ \left\{ \begin{array} \ u′′′(t)=f(t, u (t), u′(t), u′′(t))+ e (t), \ 0 &amp;lt; t &amp;lt; 1, \\ u(0) = \sum_{i=1}^{m−2} k_iu (ξ_i), u′ (0) = u′(1) = 0, \end{array} \right.&amp;nbsp;}$$ where ${ f : (0, 1) × R^3 → R }$ is a function satisfying Carathéodory’s conditions, ${ e:(0, 1) → R \ and \ t(1 − t) e (t) ∈ L^1 [0, 1], 0 &amp;lt; ξ_1 &amp;lt; ξ_2 &amp;lt; · · · &amp;lt; ξ_{m−2} &amp;lt; 1, k_i ∈ R (i = 1, 2, . . . , m − 2) \ and }$ ${ \sum_{i=1}^{m−2} k_i \neq 1.}$ Some existence criteria of at least one solution are established by using the well-known Leray-Schauder Continuation Principle.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">3</style></issue><section><style face="normal" font="default" size="100%">353</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%">JINHAI CHEN</style></author><author><style face="normal" font="default" size="100%">DONAL O’REGAN</style></author><author><style face="normal" font="default" size="100%">CHRISTOPHER C. TISDELL</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">SOME RESULTS ON PERIODIC SOLUTIONS FOR EVEN ORDER DIFFERENTIAL EQUATIONS</style></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></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%">http://www.acadsol.eu/en/articles/12/1/3.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">12</style></volume><pages><style face="normal" font="default" size="100%">5</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 presents some new results for the existence of a unique 2π-periodic solution of even order differential equations. Here the assumption in [3, J. H. Chen and D. O’Regan, On periodic solutions for even order differential equations, Nonlinear Anal., (2007), doi: 10.1016/j.na.2007.06.013] that maximal solution of an initial value problem exists is removed.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><section><style face="normal" font="default" size="100%">23</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%">J. Diblık</style></author><author><style face="normal" font="default" size="100%">J. Bastinec</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">MULTIPOINT SINGULAR BOUNDARY-VALUE PROBLEM FOR SYSTEM OF SEMILINEAR DIFFERENTIAL EQUATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Communications in Applied Analysis</style></secondary-title><short-title><style face="normal" font="default" size="100%">Multipoint Singular Boundary-Value Problem</style></short-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></keywords><dates><year><style  face="normal" font="default" size="100%">2006</style></year><pub-dates><date><style  face="normal" font="default" size="100%">12/2006</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.acadsol.eu/en/articles/10/4/1.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">10</style></volume><pages><style face="normal" font="default" size="100%">438</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;A singular Cauchy-Nicoletti problem for system of ordinary differential equations is considered. An approach which combines topological method of T. Wazewski and Schauder’s principle is used. A theorem concerning the existence of a solution of this problem (a graph of which lies in a given domain) is proved. Moreover, estimations of its coordinates are obtained.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">4</style></issue><work-type><style face="normal" font="default" size="100%">scientific: mathematics</style></work-type><section><style face="normal" font="default" size="100%">421</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 R. Kaufmann</style></author><author><style face="normal" font="default" size="100%">NICKOLAI KOSMATOV</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A Singular Three-Point Boundary Value Problem</style></title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B10</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%">2005</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2005</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.acadsol.eu/en/articles/9/4/1.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">9</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;We study the three-point singular nonlinear boundary-value problem $${&amp;nbsp;−u ′′(t) = a(t)f(u(t)), \ \&amp;nbsp; 0 &amp;lt; t &amp;lt; 1, }$$&amp;nbsp; $${ u(0) = 0, \ \&amp;nbsp; αu(η) = u(1), }$$ where ${ 0 &amp;lt; η &amp;lt; 1, 0 &amp;lt; α &amp;lt; \frac{1}{η} }$ and ${a(t)}$ is in a class of integrable functions. Using a fixed point theorem we show that under certain growth conditions imposed on continuous ${ f(u)}$, the problem has infinitely many solutions.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">4</style></issue><section><style face="normal" font="default" size="100%">429</style></section></record></records></xml>