On Schr o<spacing diaeresis>dinger-Poisson equations with a critical nonlocal term

In this paper, we study the following non -autonomous Schr delta dinger-Poisson equation with a critical nonlocal term and a critical nonlinearity: { -triangle u+V(x)u+lambda phi|u|3u=f(u)+(u+)5,inR(3) -triangle phi=|u|5,inR(3) First, we consider the case that the nonlinearity satisfies the Berestycki-Lions type condition with critical growth. Second, we consider the case that intV-1(0) is contained in a spherical shell. By using variational methods, we obtain the existence and asymptotic behavior of positive solutions.