<?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%">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%">ANDREW CONNER</style></author><author><style face="normal" font="default" size="100%">MIN WANG</style></author><author><style face="normal" font="default" size="100%">CLAIRE ZAJACZKOWSKI</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">UNIQUENESS AND PARAMETER DEPENDENCE OF POSITIVE SOLUTIONS OF DISCRETE PERIODIC BOUNDARY VALUE PROBLEMS</style></title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B08</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%">http://www.acadsol.eu/en/articles/19/2/1.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%">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;The authors study a type of second order nonlinear discrete periodic boundary value problems. The existence and uniqueness of positive solutions are discussed. The parametric dependence of the solutions is also investigated. Two examples are given as applications of the results.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">2</style></issue><section><style face="normal" font="default" size="100%">163</style></section></record></records></xml>