一类带临界指数的 Schrödinger-Newton 系统正解的存在性

数学物理学报 ›› 2023, Vol. 43 ›› Issue (5): 1373-1381.

一类带临界指数的 Schrödinger-Newton 系统正解的存在性

陈清方¹,廖家锋^1,^2,^*(),元艳香³

¹西华师范大学数学与信息学院四川南充 637009
²西华师范大学公共数学学院四川南充 637009
³黔南名族师范学院数学与统计学院贵州都匀 55800

收稿日期:2022-09-05 修回日期:2023-04-10 出版日期:2023-10-26 发布日期:2023-08-09
通讯作者: 廖家锋 E-mail:liaojiafeng@163.com
基金资助:
四川省科技厅自然科学项目(2023NSFSC0073);西华师范大学基本科研项目(18B015);贵州省教育厅青年科技人才成长项目(黔教合 KY 字 [2016]316)

Existence of Positive Solutions for a Class of Schrödinger-Newton Systems with Critical Exponent

Cheng Qingfang¹,Liao Jiafeng^1,^2,^*(),Yuan Yanxiang³

¹School of Mathematics and Information, China West Normal University, Sichuan Nanchong 637009
²College of Mathematics Education, China West Normal University, Sichuan Nanchong 637009
³School of Mathematics and Statistics, Qiannan Normal University for Nationaliyies, Guizhou Duyun 558000

Received:2022-09-05 Revised:2023-04-10 Online:2023-10-26 Published:2023-08-09
Contact: Jiafeng Liao E-mail:liaojiafeng@163.com
Supported by:
Natural Science Foundation of Sichuan(2023NSFSC0073);Fundamental Research Funds of China West Normal University(18B015);Young Science and Technology Scholars of Guizhou Provincial Department of Education (KY2016316)

摘要/Abstract

摘要：

该文在有界区域研究了一类含临界指数的 Schrödinger-Newton 系统正解的存在性. 运用变分方法, 获得了该系统至少存在两个正解.

关键词: Schr?dinger-Newton 系统, 临界指数, 山路引理, 正解

Abstract:

In this paper, we study the existence of positive solutions for a class of Schrödinger-Newton system with critical exponents on bounded domain, and obtain two positive solutions by the variational method.

Key words: Schr?dinger-Newton system, Critical exponent, Mountain pass theorem, Positive solutions

中图分类号:

O177.91

陈清方,廖家锋,元艳香. 一类带临界指数的 Schrödinger-Newton 系统正解的存在性[J]. 数学物理学报, 2023, 43(5): 1373-1381.

Cheng Qingfang,Liao Jiafeng,Yuan Yanxiang. Existence of Positive Solutions for a Class of Schrödinger-Newton Systems with Critical Exponent[J]. Acta mathematica scientia,Series A, 2023, 43(5): 1373-1381.

参考文献 11

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