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

被引：231

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.

引用

页码：1219 / 1242

页数：24

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