<?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%">YANG WU</style></author><author><style face="normal" font="default" size="100%">JIAN-PING SUN</style></author><author><style face="normal" font="default" size="100%">YA-HONG ZHAO</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">POSITIVE SOLUTIONS OF A FOURTH-ORDER PERIODIC BOUNDARY VALUE PROBLEM WITH PARAMETER</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B15</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">07/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/27/3/12.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">27</style></volume><pages><style face="normal" font="default" size="100%">16</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, we study the following periodic boundary value problem of fourth-order ordinary differential equation&lt;br /&gt;
&amp;nbsp; \begin{equation*}&lt;br /&gt;
&amp;nbsp; \left\{&lt;br /&gt;
&amp;nbsp; &amp;nbsp;\begin{aligned}&lt;br /&gt;
&amp;nbsp; &amp;nbsp;&amp;amp;u^{(4)}(t)+\alpha u^{\prime\prime}(t)-\rho^{4}u(t)+\lambda f(t,u(t))=0,~t\in{[0,2\pi]},\\&lt;br /&gt;
&amp;nbsp; &amp;nbsp;&amp;amp;u^{(i)}(0)=u^{(i)}(2\pi),~i=0,1,2,3,\\&lt;br /&gt;
&amp;nbsp; &amp;nbsp;\end{aligned}&lt;br /&gt;
&amp;nbsp; &amp;nbsp;\right.&lt;br /&gt;
&amp;nbsp; \end{equation*}&lt;br /&gt;
where $\alpha$ and $\rho$ are constants satisfying $\rho\neq0$ and $4\alpha+16\rho^{4}&amp;lt;1$, and $\lambda&amp;gt;0$ is a parameter. By imposing some conditions on the nonlinear term $f$, we obtain the existence and multiplicity of positive solutions to the above problem for suitable $\lambda$. The main tool used is Guo-Krasnoselskii fixed point theorem.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">33</style></issue><section><style face="normal" font="default" size="100%">637</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%">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></records></xml>