Existence of positive ground state solutions of critical nonlinear Klein–Gordon–Maxwell systems

Abstract

In this paper we study the following nonlinear Klein–Gordon–Maxwell system { − Δ u + [ m 0 2 − ( ω + φ ) 2 ] u = f ( u ) in   R 3 , Δ φ = ( ω + φ ) u in   R 3 , where 0 < ω < m 0 . Based on an abstract critical point theorem established by Jeanjean, the existence of positive ground state solutions is proved, when the nonlinear term f ( u ) exhibits linear near zero and a general critical growth near infinity. Compared with other recent literature, some different arguments have been introduced and some results are extended.