Abstract：In this talk, we give some recent results on the existence of ground state for nonlinear Schr?dinger-Poisson-Slater equation with unbounded potential. By using Ekeland’s variational principle we prove that there exists a ground state with negative energy level. For the special case of Schr?dinger-Poisson-Slater equation with harmonic potential, we show that the ground state must be nonradial.