Infinitely many large energy solutions of nonlinear Schr$ddot{o}$dinger-Maxwell system
Journal: NEW TRENDS IN MATHEMATICAL SCIENCES (Vol.2, No. 2)Publication Date: 2014-09-30
Authors : Mohsen Alimohammady; Morteza Koozehgar Kalleji;
Page : 87-94
Keywords : Schr$\ddot{o}$dinger-Maxwell equations variational methods Strongly indefinite functionals Cerami conditions;
Abstract
This paper deals with the existence of infinitely many large energy solutions for nonlinear Schr$ddot{o}$dinger-Maxwell system [ left{begin{array}{ll} -Delta u + V(x)u + lambdaphi u = |u|^{p - 1}u &textrm{ in } mathbb{R}^{3} \ -Delta phi = u^{2} &textrm{ in } mathbb{R}^{3} , end{array}right.] We use the Fountain theorem under Cerami conditions ref{th.1} to find infinitely many large solutions for $pin (2 , 6)$ and $lambda in mathbb{R}^{+} - (frac{4}{7} , frac{4}{3})$.
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