Improved results for Klein–Gorden–Maxwell systems with critical growth

Abstract

In this paper we consider the following Klein–Gorden–Maxwell system −Δu+V0u−(2w+ϕ)ϕu=λ|u|p−2u+|u|4u,x∈R3,Δϕ=(w+ϕ)u2,x∈R3,where λ, w and V0 are positive real constants. By employing some analytical skills and using the variational method, we prove some results about the existence of ground state solutions for the system under a general condition imposed on V0. Our results improve and extend some related ones in the literature.