<?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%">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%">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>