On ground state solutions for the Schrödinger-Poisson equations with critical growth

In this paper, we study the existence of ground state solutions for the following Schrödinger-Poisson equation{−Δu+V(x)u+λϕu=μ|u|q−1u+|u|4u,inR3,−Δϕ=u2,inR3, where μ is a positive parameter. Under some certain assumptions on V, we prove that for every λ>0 and q∈(2,5), such a class of Schrödinger-Poisson equation with critical growth has at least a positive ground state solution via variational methods. Some recent results from the literature are extended.