Ground state solution for a Schrödinger-Poisson equation with critical growth

In this paper, we consider the following nonlinear Schrödinger-Poissonequation −△u+V(x)u+K(x)ϕu=μa(x)|u|q−1u+|u|4u,inR3,−△ϕ=K(x)u2,inR3,where μ is a positive parameter. Under certain assumptions on V(x), K(x) and a(x), we prove that for every μ>0 and q∈(2,5), the Schrödinger-Poisson equation with critical growth has at least a positive ground state solution by variational method.