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http://dx.doi.org/10.4134/JKMS.j160344

EXISTENCE AND MULTIPLICITY OF NONTRIVIAL SOLUTIONS FOR KLEIN-GORDON-MAXWELL SYSTEM WITH A PARAMETER  

Che, Guofeng (School of Mathematics and Statistics, Central South University)
Chen, Haibo (School of Mathematics and Statistics, Central South University)
Publication Information
Journal of the Korean Mathematical Society / v.54, no.3, 2017 , pp. 1015-1030 More about this Journal
Abstract
This paper is concerned with the following Klein-Gordon-Maxwell system: $$\{-{\Delta}u+{\lambda}V(x)u-(2{\omega}+{\phi}){\phi}u=f(x,u),\;x{\in}\mathbb{R}^3,\\{\Delta}{\phi}=({\omega}+{\phi})u^2,\;x{\in}\mathbb{R}^3$$ where ${\omega}$ > 0 is a constant and ${\lambda}$ is the parameter. Under some suitable assumptions on V (x) and f(x, u), we establish the existence and multiplicity of nontrivial solutions of the above system via variational methods. Our conditions weaken the Ambrosetti Rabinowitz type condition.
Keywords
Klein-Gordon-Maxwell system; Sobolev embedding; variational methods; infinitely many solutions;
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