ON THE HARDY-LITTLEWOOD-SOBOLEV TYPE SYSTEMS

被引：12

作者：

Cheng, Ze ^{[1
]}

Huang, Genggeng ^{[2
,3
]}

Li, Congming ^{[1
,2
,3
]}

机构：

[1] Univ Colorado, Dept Appl Math, Boulder, CO 80309 USA

[2] Shanghai Jiao Tong Univ, Dept Math, INS, Shanghai, Peoples R China

[3] Shanghai Jiao Tong Univ, MOE LSC, Shanghai, Peoples R China

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2016年 / 15卷 / 06期

基金：

美国国家科学基金会;

关键词：

Hardy-Littlewood-Sobolev; existence; non-existence; uniqueness; LIOUVILLE-TYPE; CLASSIFICATION; EXISTENCE; EQUATIONS;

D O I：

10.3934/cpaa.2016027

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study some qualitative properties of Hardy-Littlewood-Sobolev type systems. The HLS type systems are categorized into three cases: critical, supercritical and subcritical. The critical case, the well known original HLS system, corresponds to the Euler-Lagrange equations of the fundamental HLS inequality. In each case, we give a brief survey on some important results and useful methods. Some simplifications and extensions based on somewhat more direct and intuitive ideas are presented. Also, a few new qualitative properties are obtained and several open problems are raised for future research.

引用

页码：2059 / 2074

页数：16

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[2]

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[3]

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