The Brezis-Nirenberg type critical problem for the nonlinear Choquard equation

被引：225
|
作者：
Gao, Fashun [1 ]
Yang, Minbo [1 ]
机构：
[1] Zhejiang Normal Univ, Dept Math, Jinhua 321004, Peoples R China
来源：
SCIENCE CHINA-MATHEMATICS | 2018年 / 61卷 / 07期
基金：
中国国家自然科学基金;
关键词：
Brezis-Nirenberg problem; Choquard equation; Hardy-Littlewood-Sobolev inequality; critical exponent; CRITICAL SOBOLEV EXPONENTS; GROUND-STATE SOLUTIONS; ELLIPTIC PROBLEMS; SCHRODINGER-EQUATION; EXISTENCE; MULTIPLICITY;
D O I：
10.1007/s11425-016-9067-5
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We establish some existence results for the Brezis-Nirenberg type problem of the nonlinear Choquard equation -. u = ( O | u (y)| 2 | x - y | d y) | u | 2 2 u + u in O; where Omega is a bounded domain of R (N) with Lipschitz boundary, lambda is a real parameter, N 3, is the critical exponent in the sense of the Hardy-Littlewood-Sobolev inequality.
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页码：1219 / 1242
页数：24
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