Ground state solutions for some Schrödinger–Poisson systems with periodic potentials

Abstract

In this paper, we consider the following nonlinear Schrödinger–Poisson system{−Δu+V(x)u+ϕu=f(x,u),inR3,−Δϕ=u2,inR3, where the nonlinearity f is superlinear at infinity with subcritical or critical growth and V is positive, continuous and periodic in x. The existence of ground state solutions, i.e., nontrivial solutions with least possible energy of this system is obtained. Moreover, when V≡1, we obtain ground state solutions for the above system with a wide class of superlinear nonlinearities by using a new approach.