Semiclassical states for Schrödinger-Poisson system with Hartree-type nonlinearity

Abstract

In this paper we are interested in a class of semiclassical Schrödinger-Poisson system with Hartree-type nonlinearity. Firstly, we prove the existence of groundstate for autonomous system by using the subcritical approximation and the Pohozaev constraint method. Secondly, we prove the existence of semiclassical state solutions and multiplicity for system with critical frequency by using the genus. Finally, we study multiplicity and concentration behavior for solutions of system with general potential by using the Lusternik-Schnirelman theory.