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

doi:10.1007/s10473-021-0304-0

数学物理学报(英文版) ›› 2021, Vol. 41 ›› Issue (3): 703-711.doi: 10.1007/s10473-021-0304-0

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

蒋永生¹, 魏娜¹, 吴永洪²

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

收稿日期:2019-09-03 修回日期:2020-05-02 出版日期:2021-06-25 发布日期:2021-06-07
通讯作者: Na WEI E-mail:nawei2006@126.com
作者简介:Yongsheng JIANG,E-mail:jiangys@zuel.edu.cn;Yonghong WU,E-mail:Y.Wu@curtin.edu.au
基金资助:
This research was supported by NSFC (11871386 and 12071482) and the Natural Science Foundation of Hubei Province (2019CFB570).

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

Yongsheng JIANG¹, Na WEI¹, Yonghong WU²

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).

摘要/Abstract

摘要： We are concerned with the nonlinear Schrödinger-Poisson equation \begin{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. \end{equation} 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).

关键词: Multiple solutions, ground state solution, Schr?dinger-Poisson equation

Abstract: We are concerned with the nonlinear Schrödinger-Poisson equation \begin{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. \end{equation} 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).

Key words: Multiple solutions, ground state solution, Schr?dinger-Poisson equation

中图分类号:

35J20

蒋永生, 魏娜, 吴永洪. MULTIPLE SOLUTIONS FOR THE SCHRÖDINGER-POISSON EQUATION WITH A GENERAL NONLINEARITY[J]. 数学物理学报(英文版), 2021, 41(3): 703-711.

Yongsheng JIANG, Na WEI, Yonghong WU. MULTIPLE SOLUTIONS FOR THE SCHRÖDINGER-POISSON EQUATION WITH A GENERAL NONLINEARITY[J]. Acta mathematica scientia,Series B, 2021, 41(3): 703-711.

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

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

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