数学物理学报 ›› 2021, Vol. 41 ›› Issue (3): 702-722.

• 论文 • 上一篇    下一篇

带有临界增长或超临界增长的分数阶Choquard方程解的存在性和多重性

杨先勇1,2(),唐先华2,*(),顾光泽3()   

  1. 1 云南民族大学预科教育学院 昆明 650500
    2 中南大学数学与统计学院 长沙 410205
    3 云南师范大学数学学院 昆明 650500
  • 收稿日期:2020-03-31 出版日期:2021-06-01 发布日期:2021-06-09
  • 通讯作者: 唐先华 E-mail:ynyangxianyong@163.com;tangxh@mail.csu.edu.cn;guangzegu@163.com
  • 作者简介:杨先勇, E-mail: ynyangxianyong@163.com|顾光泽, E-mail: guangzegu@163.com
  • 基金资助:
    国家自然科学基金(11971485);国家自然科学基金(11661083);国家自然科学基金(11861078);国家自然科学基金(11771385);国家自然科学基金(11901345);湖南省研究生科研创新基金和中南大学中央高校基本科研业务费专项资金

Existence and Multiplicity of Solutions for a Fractional Choquard Equation with Critical or Supercritical Growth

Xianyong Yang1,2(),Xianhua Tang2,*(),Guangze Gu3()   

  1. 1 School of Preparatory Education, Yunnan Minzu University, Kunming 650500
    2 School of Mathematics and Statistics, Central South University, Changsha 410205
    3 School of Mathematics, Yunnan Normal University, Kunming 650500
  • Received:2020-03-31 Online:2021-06-01 Published:2021-06-09
  • Contact: Xianhua Tang E-mail:ynyangxianyong@163.com;tangxh@mail.csu.edu.cn;guangzegu@163.com
  • Supported by:
    the NSFC(11971485);the NSFC(11661083);the NSFC(11861078);the NSFC(11771385);the NSFC(11901345);the Hunan Provincial Innovation Foundation for Postgraduate and the Fundamental Research Funds for the Central Universities of Central South University

摘要:

该文考虑如下带有临界增长或超临界增长的分数阶Choquard方程 其中s(01)μ(0N)N>2sq2μsf是一个连续函数.众所周知,在Hardy-Littlewood-Sobolev不等式意义下,2μs=2NμN2s2μs=2NμN分别是上述方程的上、下临界指数.许多解的存在性结果都要求q[2μs2μs].在此,该文研究上述方程临界增长或超临界增长的情形.当f满足适当的条件时,通过利用一些分析技巧,上述方程解的存在性和多重性将被证明.

关键词: 分数阶Choquard方程, 临界增长, 超临界增长, 截断技巧

Abstract:

We consider the following fractional Choquard equation with critical or supercritical growth where s(0,1), μ(0,N), N>2s, q2μ,s, f is a continuous function. It is well-known that 2μ,s=2NμN2s and 2μ,s=2NμN are critical exponents for the above equation in the sense of Hardy-Littlewood-Sobolev inequality. Many existence results have been established for q[2μ,s,2μ,s] in recent years. Here we are interested in critical or supercritical case for the above equation. Under some assumptions of f, the existence and multiplicity of solutions for the above equation can be obtained by applying some analytical techniques.

Key words: Fractional Choquard equation, Critical, Supercritical growth, Truncation technique

中图分类号: 

  • O175.2