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.

Keywords:

• Ground state solitary waves
• planar Schrödinger–Poisson system

AMS Subject Classifications:

• 35J50
• 35Q40

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research is supported by the Shanghai Natural Science Foundation [Project number 15ZR1429500].