In this paper we study the following nonlinear Klein–Gordon–Maxwell system −∆u + [m2 0 − (ω + φ) 2 ]u = f(u) in R3 ∆φ = (ω + φ)u in R3 where 0 < ω < m0. 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
