<?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%">John R. Graef</style></author><author><style face="normal" font="default" size="100%">LINGJU KONG</style></author><author><style face="normal" font="default" size="100%">QINGKAI KONG</style></author><author><style face="normal" font="default" size="100%">MIN WANG</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A FRACTIONAL BOUNDARY VALUE PROBLEM WITH DIRICHLET BOUNDARY CONDITION</style></title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B15</style></keyword><keyword><style  face="normal" font="default" size="100%">34B27</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2015</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.acadsol.eu/en/articles/19/4/2.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%">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, the authors study a nonlinear fractional boundary value problem consisting of the equation$${ −D^α_{0+}u + aD^β_{0+}u = w(t)f(u), \ \ \ 1 &amp;lt; α &amp;lt; 2, 0 ≤ β &amp;lt; 1, }$$ and the Dirichlet boundary condition. The associated Green’s function is derived in terms of the generalized Mittag-Leffler function, and the existence of solutions is established based on it.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">4</style></issue><section><style face="normal" font="default" size="100%">497</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%">LINGJU KONG</style></author><author><style face="normal" font="default" size="100%">MIN WANG</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">INFINITELY MANY HOMOCLINIC SOLUTIONS FOR SECOND ORDER DIFFERENCE EQUATIONS WITH p-LAPLACIAN</style></title></titles><keywords><keyword><style  face="normal" font="default" size="100%">37C20</style></keyword><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword><keyword><style  face="normal" font="default" size="100%">58E0</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/19/1/7.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%">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;By using critical point theory, the authors study the existence of infinitely many homoclinic solutions to the difference equation $${ −∆a(k)\phi_p(∆u(k − 1))&amp;nbsp;+ b(k)\phi_p(u(k)) = λf(k, u(k))), \ \&amp;nbsp; k ∈ \mathbb{Z} }$$, where ${p &amp;gt; 1}$ is a real number, ${ \phi_p(t) = |t|^{p−2} t}$&amp;nbsp; for ${ t ∈ \mathbb{R},\ \ λ &amp;gt; 0}$ is a parameter, ${ a, b : \mathbb{Z} → (0, ∞), }$ and ${ f : \mathbb{Z} × \mathbb{R} → \mathbb{R} }$ is a continuous function in the second variable. Some known work in the literature is extended.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><section><style face="normal" font="default" size="100%">95</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%">LINGJU KONG</style></author><author><style face="normal" font="default" size="100%">MIN WANG</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">TWO NONTRIVIAL SOLUTIONS FOR A DISCRETE FOURTH ORDER PERIODIC BOUNDARY VALUE PROBLEM</style></title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B08</style></keyword><keyword><style  face="normal" font="default" size="100%">34B15</style></keyword><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword><keyword><style  face="normal" font="default" size="100%">58E3</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/19/4/1.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;We study the discrete fourth order periodic boundary value problem with a parameter $${ \left\{ \begin{array}{1}∆^4u(t − 2) − ∆ \left(p(t − 1)∆_u(t − 1)\right)&amp;nbsp;+ q(t)u(t) = λf(t, u(t)), \ t ∈ [1, N]_Z,\\&amp;nbsp;∆^iu(−1) = ∆^iu(N − 1), \ \&amp;nbsp; &amp;nbsp;i = 0, 1, 2, 3.\end{array}\right. }$$ By using variational methods and the mountain pass lemma, sufficient conditions are found under which the above problem has at least two nontrivial solutions. One example is included to illustrate the result.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">4</style></issue><section><style face="normal" font="default" size="100%">487</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%">LINGJU KONG</style></author><author><style face="normal" font="default" size="100%">QINGKAI KONG</style></author><author><style face="normal" font="default" size="100%">BO YANG</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">HIGHER ORDER BOUNDARY VALUE PROBLEMS WITH TWO POINT SEPARATED NONHOMOGENEOUS BOUNDARY CONDITIONS</style></title></titles><keywords><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%">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/15/4/2.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&gt;The authors study the 2n-th order nonlinear boundary value problems with two point separated nonhomogeneous boundary conditions u (2n) = g(t)f(t, u), t ∈ (0, 1),    αu(2i) (0) − βu(2i+1)(0) = (−1)iλ2i , γu(2i) (1) + δu(2i+1)(1) = (−1)iλ2i+1. i = 0, . . . , n − 1, Criteria are established for the existence of nontrivial solutions, positive solutions, and negative solutions of the above problem. Conditions are determined by the relationship between the behavior of the quotient f(t, x)/x for x near 0 and ∞, and the smallest positive characteristic values of some associated linear integral operator. This work improves and extends a number of recent results in the literature on this topic. The results are illustrated with examples.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">4</style></issue><section><style face="normal" font="default" size="100%">435</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%">LINGJU KONG</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">POSITIVE PERIODIC SOLUTIONS FOR SYSTEMS OF FUNCTIONAL 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%">POSITIVE PERIODIC SOLUTIONS</style></short-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34K13</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%">04/2010</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.acadsol.eu/en/articles/14/2/2.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">14</style></volume><pages><style face="normal" font="default" size="100%">154</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;We consider classes of systems of first order functional differential equations. Criteria are established for the existence of positive T -periodic solutions of the systems under consideration. One example is also included to illustrate the applications of our results.&lt;/div&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%">137</style></section></record></records></xml>