数学物理学报 ›› 2024, Vol. 44 ›› Issue (1): 101-119.

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一类非局部临界椭圆方程组高能量解的多重性

付培源(),夏阿亮*()   

  1. 江西师范大学数学与统计学院 南昌 330022
  • 收稿日期:2023-01-05 修回日期:2023-04-13 出版日期:2024-02-26 发布日期:2024-01-10
  • 通讯作者: 夏阿亮, E-mail:aliang_xia@jxnu.edu.cn
  • 作者简介:付培源, E-mail:2398570050@qq.com
  • 基金资助:
    国家自然科学基金(12161044);江西省自然科学基金(20224ACB218001);江西省自然科学基金(20212BAB211013);江西省自然科学基金(20224BCD41001)

Multiplicity of High Energy Solutions for a Class of Nonlocal Critical Elliptic System

Fu Peiyuan(),Xia Aliang()   

  1. School of Mathematics and Statistics, Jiangxi Normal University, Nanchang 330022
  • Received:2023-01-05 Revised:2023-04-13 Online:2024-02-26 Published:2024-01-10
  • Supported by:
    NSFC(12161044);Jiangxi Province Natural Science Foundation(20224ACB218001);Jiangxi Province Natural Science Foundation(20212BAB211013);Jiangxi Province Natural Science Foundation(20224BCD41001)

摘要:

利用变分方法, 结合拓扑度理论, 该文证明了一类带有 Hardy-Littlewood-Sobolev 临界指标的椭圆方程组至少存在两个正的高能量解.

关键词: 非局部椭圆方程组, Hardy-Littlewood-Sobolev 临界指标, 变分法, 拓扑度

Abstract:

By using variational methods and topological degree theory, this paper proved a class of coupled nonlocal elliptic system involving the Hardy-Littlewood-Sobolev critical exponents has at least two positive high energy solutions.

Key words: Nonlocal elliptic system, Hardy-Littlewood-Sobolev critical exponents, Variational methods, Topological degree theory

中图分类号: 

  • O175