Multiplicity of Solutions for a Nonlinear Klein-Gordon-Maxwell System

Abstract

In this paper we study the nonlinear Klein-Gordon-Maxwell system $$\left \{\begin{array}{l@{\quad}l} -\Delta u+V(x)u-(2\omega+\phi)\phi u=f(x,u),&x\in{\mathbb{R}}^3,\\ \Delta \phi=(\omega+\phi)u^2,&x\in{\mathbb{R}}^3. \end{array} \right . $$ By means of a variant fountain theorem and the symmetric mountain pass theorem, we obtain the existence of infinitely many large energy solutions.