Ground state solitary waves for the planar Schrödinger-Poisson system

Abstract

In this paper, we investigate the planar Schrödinger–Poisson System. Based on fixed point argument, Riesz’s rearrangement, Hardy–Littlewood–Sobolev inequality and critical point theory, we prove the existence and symmetry properties of ground state solitary waves. In addition to their existence, we also obtain the orbital stability of solitary waves.