Abstract:

This article concerns the following Klein-Gordon-Maxwell system $ \left\{ \begin{array}{*{35}{l}} -\Delta u+\lambda V(x)u-K(x)(2\omega +\phi )\phi u=f(x,u), & x\in {{\mathbb{R}}^{3}}, \\ \Delta \phi =K(x)(\omega +\phi ){{u}^{2}}, & x\in {{\mathbb{R}}^{3}}, \\\end{array} \right. $ where $ \omega> 0 $ is a constant and $ \lambda\geq1 $ is a parameter. When the nonlinearity satisfies asymptotically linear growth at infinity, the existence result of positive solutions for the system is obtained via variational methods. Our result completes some recent works concerning the existence of solutions of this system.

Key words: Klein-Gordon-Maxwell system, Variational methods, Asymptotically linear, Positive solutions