# 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)
• Published : 2017.05.01
• 73 19

#### 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

#### Acknowledgement

Supported by : Natural Science Foundation of China

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