<?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%">LESZEK GASINSKI</style></author><author><style face="normal" font="default" size="100%">NIKOLAOS  PAPAGEORGIOU</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">PAIRS OF NONTRIVIAL SOLUTIONS FOR RESONANT ROBIN PROBLEMS WITH INDEFINITE LINEAR PART</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%">35J20</style></keyword><keyword><style  face="normal" font="default" size="100%">35J60</style></keyword><keyword><style  face="normal" font="default" size="100%">58E05</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%">2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/26/2/6.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</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;We study a semilinear Robin problem driven by the Laplacian plus an indefinite and unbounded potential and a Carath´eodory reaction term which exhibits linear growth near ±∞ and near zero. Resonance with respect to different eigenvalues can occur at both ±∞ and near zero. Using the saddle point reduction method and Morse theory (critical groups), we prove a multiplicity theorem producing two nontrivial smooth solutions.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">2</style></issue><section><style face="normal" font="default" size="100%">309</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%">LESZEK GASINSKI</style></author><author><style face="normal" font="default" size="100%">NIKOLAOS  PAPAGEORGIOU</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">PARAMETRIC p-LAPLACIAN EQUATIONS WITH SUPERLINEAR REACTIONS</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%">35J20</style></keyword><keyword><style  face="normal" font="default" size="100%">35J60</style></keyword><keyword><style  face="normal" font="default" size="100%">35J92</style></keyword><keyword><style  face="normal" font="default" size="100%">58E05</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%">https://acadsol.eu/dsa/articles/24/41-DSA-523-558.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">24</style></volume><pages><style face="normal" font="default" size="100%">36</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 a parametric nonlinear Dirichlet problem driven by the p-Laplacian and with a Carath´eodory reaction which is (p − 1)-superlinear near ±∞ (but without satisfying the Ambrosetti-Rabinowitz condition) and (p − 1)-sublinear near zero. We show that for all values of the parameter λ &amp;gt; 0, the problem has at least three nontrivial solutions (two of constant sign). If we alter the geometry near the origin by introducing a “concave” nonlinearity (problem with combined nonlinearities), we show the existence of at least five nontrivial solutions (four of constant sign and the fifth nodal), when the parameter λ &amp;gt; 0 is small. Also, we produce extremal constant sign solutions u&lt;sup&gt;∗&lt;/sup&gt;&lt;sub&gt;λ&lt;/sub&gt; ∈ -int C&lt;sub&gt;+&lt;/sub&gt; and v&lt;sup&gt;∗&lt;/sup&gt;&lt;sub&gt;λ&lt;/sub&gt; ∈ −int C+. We investigate the monotonicity and continuity properties of the map λ→ u&lt;sup&gt;∗&lt;/sup&gt;&lt;sub&gt;λ&lt;/sub&gt; .&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">523</style></section></record></records></xml>