Nontrivial solutions for Klein–Gordon–Maxwell systems with sign-changing potentials

Abstract

Abstract This paper is concerned with the nonlinear Klein–Gordon–Maxwell systems. Unlike all known results in the literature, the Schrödinger operator − Δ + V $-\Delta +V$ is allowed to be indefinite and the weaker superlinear conditions are imposed instead of the common 4-superlinear conditions on f. By combining a local linking argument and Morse theory, we obtain that the system admits a nontrivial solution.

Keywords

• Klein–Gordon–Maxwell systems
• Sign-changing potential
• Morse theory
• Variational methods