Abstract:

This article concerns the following Klein-Gordon-Maxwell system $\begin{equation*} \begin{cases} -\Delta u+ V(x)u-(2\omega+\phi)\phi u=f(x,u)+K(x)|u|^{s-2}u, & x\in \mathbb{R}^{3},\\ \Delta \phi=(\omega+\phi)u^2, & x\in \mathbb{R}^{3}, \end{cases} \end{equation*}$ where $\omega> 0$ is a constant. When $f$ satisfies local condition just in a neighborhood of the origin, existence and multiplicity of nontrivial solutions can be proved via variational methods and Moser iteration. Our result completes some recent works concerning research on solutions of this system.

Key words: Klein-Gordon-Maxwell system, variational methods, moser iteration, nontrivial solutions