This paper is concerned with the nonlinear Klein–Gordon–Maxwell system {−Δz+V(x)z−(2ω+ϕ)ϕz=g(x,z)x∈R3,Δϕ=(ω+ϕ)z2x∈R3, where the potential V and the primitive of g are both allowed to be sign-changing. Under more general superlinear assumptions on the nonlinearity, we obtain a new existence result of infinitely many high energy solutions by using variational methods. Some recent results in the literature are generalized and sig...