SIGN-CHANGING SOLUTIONS FOR THE NONLINEAR SCHRÖDINGER-POISSON SYSTEM WITH CRITICAL GROWTH*

doi:10.1007/s10473-023-0521-9

数学物理学报(英文版) ›› 2023, Vol. 43 ›› Issue (5): 2291-2308.doi: 10.1007/s10473-023-0521-9

SIGN-CHANGING SOLUTIONS FOR THE NONLINEAR SCHRÖDINGER-POISSON SYSTEM WITH CRITICAL GROWTH^*

Yinbin Deng, Wei Shuai^†, Xiaolong Yang

School of Mathematics and Statistics & Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan 430079, China;; School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China

收稿日期:2021-09-09 修回日期:2023-04-08 发布日期:2023-10-25

SIGN-CHANGING SOLUTIONS FOR THE NONLINEAR SCHRÖDINGER-POISSON SYSTEM WITH CRITICAL GROWTH^*

Yinbin Deng, Wei Shuai^†, Xiaolong Yang

School of Mathematics and Statistics & Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan 430079, China;; School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China

Received:2021-09-09 Revised:2023-04-08 Published:2023-10-25
Contact: †Wei Shuai, wshuai@mail.ccnu.edu.cn
About author:Yinbin Deng, E-mail: ybdeng@mail.ccnu.edu.cn; Xiaolong Yang, E-mail: yangxiaolong@mails.ccnu.edu.cn
Supported by:
National Natural Science Foundation of China (12071170, 11961043, 11931012, 12271196). Yang’s research was also supported by the excellent doctoral dissertation cultivation grant (2022YBZZ034) from Central China Normal University.

摘要/Abstract

摘要： In this paper, we study the following Schrödinger-Poisson system with critical growth: \begin{equation*} \begin{cases}-\Delta u+V(x)u+ \phi(x)u =f(u)+|u|^4u, \ & x\in\mathbb{R}^3, \\ -\Delta \phi=u^2, \ & x\in\mathbb{R}^3. \end{cases} \end{equation*} We establish the existence of a positive ground state solution and a least energy sign-changing solution, providing that the nonlinearity $f$ is super-cubic, subcritical and that the potential $V(x)$ has a potential well.

关键词: Schrödinger-Poisson system, ground state solution, sign-changing solution, critical growth

Abstract: In this paper, we study the following Schrödinger-Poisson system with critical growth: \begin{equation*} \begin{cases}-\Delta u+V(x)u+ \phi(x)u =f(u)+|u|^4u, \ & x\in\mathbb{R}^3, \\ -\Delta \phi=u^2, \ & x\in\mathbb{R}^3. \end{cases} \end{equation*} We establish the existence of a positive ground state solution and a least energy sign-changing solution, providing that the nonlinearity $f$ is super-cubic, subcritical and that the potential $V(x)$ has a potential well.

Key words: Schrödinger-Poisson system, ground state solution, sign-changing solution, critical growth

中图分类号:

35A01

Yinbin Deng, Wei Shuai, Xiaolong Yang. SIGN-CHANGING SOLUTIONS FOR THE NONLINEAR SCHRÖDINGER-POISSON SYSTEM WITH CRITICAL GROWTH^*[J]. 数学物理学报(英文版), 2023, 43(5): 2291-2308.

Yinbin Deng, Wei Shuai, Xiaolong Yang. SIGN-CHANGING SOLUTIONS FOR THE NONLINEAR SCHRÖDINGER-POISSON SYSTEM WITH CRITICAL GROWTH^*[J]. Acta mathematica scientia,Series B, 2023, 43(5): 2291-2308.

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SIGN-CHANGING SOLUTIONS FOR THE NONLINEAR SCHRÖDINGER-POISSON SYSTEM WITH CRITICAL GROWTH^*

SIGN-CHANGING SOLUTIONS FOR THE NONLINEAR SCHRÖDINGER-POISSON SYSTEM WITH CRITICAL GROWTH^*

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