Classification of solutions for a system of integral equations

被引：215

作者：

Chen, WX

Li, CM ^{[1
]}

Ou, B

机构：

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

[2] Univ Toledo, Dept Math, Toledo, OH 43606 USA

[3] Yeshiva Univ, Dept Math, New York, NY 10033 USA

来源：

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS | 2005年 / 30卷 / 1-3期

基金：

美国国家科学基金会;

关键词：

Hardy-Littlewood-Sobolev inequalities; systems of integral equations; radial symmetry; monotonicity; moving planes in integral forms;

D O I：

10.1081/PDE-200044445

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Under the natural integrability conditions u is an element of LP+1 (R-n) and v is an element of Lq+1 (R-n), we prove that all the solutions are radially symmetric and monotonic decreasing about some point. To prove this result, we introduce an integral form of the method of moving planes that is quite different front the traditional method of moving planes for PDES. We expect to see applications of this new method to many problems.

引用

页码：59 / 65

页数：7

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