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

Abstract In this paper we consider the following Klein–Gorden–Maxwell system − Δ u + V 0 u − ( 2 w + ϕ ) ϕ u = λ | u | p − 2 u + | u | 4 u , x ∈ R 3 , Δ ϕ = ( w + ϕ ) u 2 , x ∈ R 3 , where λ , w and V 0 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 V 0 . Our results improve and extend some related ones in the literature.

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