GROUND STATE SOLUTIONS FOR A SCHRÖDINGER-POISSON SYSTEM WITH UNCONVENTIONAL POTENTIAL

doi:10.1007/s10473-020-0404-2

数学物理学报(英文版) ›› 2020, Vol. 40 ›› Issue (4): 934-944.doi: 10.1007/s10473-020-0404-2

GROUND STATE SOLUTIONS FOR A SCHRÖDINGER-POISSON SYSTEM WITH UNCONVENTIONAL POTENTIAL

杜瑶^1,2, 唐春雷¹

1. School of Mathematics and Statistics, Southwest University, Chongqing 400715, China;
2. School of Mathematical Sciences, Capital Normal University, Beijing 100048, China

收稿日期:2019-06-24 修回日期:2019-10-31 出版日期:2020-08-25 发布日期:2020-08-21
通讯作者: Chunlei TANG E-mail:tangcl@swu.edu.cn
作者简介:Yao DU,E-mail:1052591976@qq.com
基金资助:
The second author was supported by National Natural Science Foundation of China (11471267) and the first author was supported by Graduate Student Scientific Research Innovation Projects of Chongqing (CYS17084).

GROUND STATE SOLUTIONS FOR A SCHRÖDINGER-POISSON SYSTEM WITH UNCONVENTIONAL POTENTIAL

Yao DU^1,2, Chunlei TANG¹

1. School of Mathematics and Statistics, Southwest University, Chongqing 400715, China;
2. School of Mathematical Sciences, Capital Normal University, Beijing 100048, China

Received:2019-06-24 Revised:2019-10-31 Online:2020-08-25 Published:2020-08-21
Contact: Chunlei TANG E-mail:tangcl@swu.edu.cn
Supported by:
The second author was supported by National Natural Science Foundation of China (11471267) and the first author was supported by Graduate Student Scientific Research Innovation Projects of Chongqing (CYS17084).

摘要/Abstract

摘要： We consider the Schrödinger-Poisson system with nonlinear term $Q(x)|u|^{p-1}u$, where the value of $\displaystyle\lim_{|x|\rightarrow\infty} Q(x)$ may not exist and $Q$ may change sign. This means that the problem may have no limit problem. The existence of nonnegative ground state solutions is established. Our method relies upon the variational method and some analysis tricks.

关键词: Schrödinger-Poisson system, ground state solutions, no limit problem

Abstract: We consider the Schrödinger-Poisson system with nonlinear term $Q(x)|u|^{p-1}u$, where the value of $\displaystyle\lim_{|x|\rightarrow\infty} Q(x)$ may not exist and $Q$ may change sign. This means that the problem may have no limit problem. The existence of nonnegative ground state solutions is established. Our method relies upon the variational method and some analysis tricks.

Key words: Schrödinger-Poisson system, ground state solutions, no limit problem

中图分类号:

35J20

杜瑶, 唐春雷. GROUND STATE SOLUTIONS FOR A SCHRÖDINGER-POISSON SYSTEM WITH UNCONVENTIONAL POTENTIAL[J]. 数学物理学报(英文版), 2020, 40(4): 934-944.

Yao DU, Chunlei TANG. GROUND STATE SOLUTIONS FOR A SCHRÖDINGER-POISSON SYSTEM WITH UNCONVENTIONAL POTENTIAL[J]. Acta mathematica scientia,Series B, 2020, 40(4): 934-944.

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GROUND STATE SOLUTIONS FOR A SCHRÖDINGER-POISSON SYSTEM WITH UNCONVENTIONAL POTENTIAL

GROUND STATE SOLUTIONS FOR A SCHRÖDINGER-POISSON SYSTEM WITH UNCONVENTIONAL POTENTIAL

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