Acta mathematica scientia,Series B ›› 2021, Vol. 41 ›› Issue (3): 703-711.

• Articles •

### MULTIPLE SOLUTIONS FOR THE SCHRÖDINGER-POISSON EQUATION WITH A GENERAL NONLINEARITY

Yongsheng JIANG1, Na WEI1, Yonghong WU2

1. 1. School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan 430073, China;
2. Department of Mathematics and Statistics, Curtin University, GPO Box U 1987, WA 6845, Australia
• Received:2019-09-03 Revised:2020-05-02 Online:2021-06-25 Published:2021-06-07
• Contact: Na WEI E-mail:nawei2006@126.com
• About author:Yongsheng JIANG,E-mail:jiangys@zuel.edu.cn;Yonghong WU,E-mail:Y.Wu@curtin.edu.au
• Supported by:
This research was supported by NSFC (11871386 and 12071482) and the Natural Science Foundation of Hubei Province (2019CFB570).

Abstract: We are concerned with the nonlinear Schrödinger-Poisson equation $$\tag{P} \left\{\begin{array}{ll} -\Delta u +(V(x) -\lambda)u+\phi (x) u =f(u), \\ -\Delta\phi = u^2,\ \lim\limits_{|x|\rightarrow +\infty}\phi(x)=0, \ \ \ x\in \mathbb{R}^3, \end{array}\right.$$ where $\lambda$ is a parameter, $V(x)$ is an unbounded potential and $f(u)$ is a general nonlinearity. We prove the existence of a ground state solution and multiple solutions to problem (P).

CLC Number:

• 35J20
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