Infinitely many standing wave solutions for the nonlinear Klein–Gordon–Maxwell system with sign-changing potential

In this paper, we study the infinitely many solutions for the nonlinear Klein–Gordon–Maxwell system {−Δu+V(x)u−(2ω+ϕ)ϕu=f(x,u),x∈R3,Δϕ=(ω+ϕ)u2,x∈R3, where ω>0ω>0 is a constant, uu, ϕ:R3→Rϕ:R3→R, the potential V(x)V(x) is allowed to be sign-changing, and the primitive of the nonlinearity ff is of super-linear growth near infinity. Our super-linear conditions are weaker than the usual super-linear conditions.