Abstract:

This article concerns the following Klein-Gordon-Maxwell system

$$\begin{cases}-\Delta u+ V(x)u-(2\omega+\phi)\phi u=\lambda |u|^{s-2}u+ f(u), & x\in \mathbb{R}^{3},\\\Delta \phi=(\omega+\phi)u^2, & x\in \mathbb{R}^{3},\end{cases}$$

where $\omega> 0$ is a constant, $\lambda> 0$ is a real parameter, $s\geq6$. When $V, f$ satisfy suitable conditions and $\lambda$ is relatively small, existence of nontrivial solution can be proved via variational methods and Moser iteration. The result in this paper completes some recent works concerning research on solutions of this system.

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