CLASSIFICATION OF SOLUTIONS FOR A CLASS OF SINGULAR INTEGRAL SYSTEM

doi:10.1016/S0252-9602(11)60330-5

数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (4): 1449-1456.doi: 10.1016/S0252-9602(11)60330-5

CLASSIFICATION OF SOLUTIONS FOR A CLASS OF SINGULAR INTEGRAL SYSTEM

许建开|谭忠

College of Sciences, Hunan Agriculture University, Changsha 410128, China； School of Mathematical Sciences, Xiamen University, Xiamen 361005, China

收稿日期:2009-07-06 出版日期:2011-07-20 发布日期:2011-07-20
通讯作者: 许建开 E-mail:xmukai@yahoo.cn；ztan85@163.com
基金资助:
Supported by National Natural Science Foundation of China-NSAF (10976026).

CLASSIFICATION OF SOLUTIONS FOR A CLASS OF SINGULAR INTEGRAL SYSTEM

XU Jian-Kai, TAN Zhong

College of Sciences, Hunan Agriculture University, Changsha 410128, China； School of Mathematical Sciences, Xiamen University, Xiamen 361005, China

Received:2009-07-06 Online:2011-07-20 Published:2011-07-20
Contact: XU Jian-Kai E-mail:xmukai@yahoo.cn；ztan85@163.com
Supported by:
Supported by National Natural Science Foundation of China-NSAF (10976026).

摘要/Abstract

摘要：

In this paper, we consider the following integral system:
???u(x) = v (y) dy,
? n n-α
R |x-y|
(1.1)
??? up(y)
?v(x) = n-μdy,
n
R |x-y|

where 0 < α, μ < n; p,q ≥ 1. Using the method of moving planes in an integral form which
was recently introduced by Chen, Li, and Ou in [2, 4, 8], we show that all positive solutions
of (0.1) are radially symmetric and decreasing with respect to some point under some
general conditions of integrability. The results essentially improve and extend previously
known results [4, 8].

关键词: Hardy-Littlewood-Sobolev inquality, integral equation, moving plane, inter-polation inequality, radial symmetry

Abstract:

Key words: Hardy-Littlewood-Sobolev inquality, integral equation, moving plane, inter-polation inequality, radial symmetry

中图分类号:

45G15

许建开, 谭忠. CLASSIFICATION OF SOLUTIONS FOR A CLASS OF SINGULAR INTEGRAL SYSTEM[J]. 数学物理学报(英文版), 2011, 31(4): 1449-1456.

XU Jian-Kai, TAN Zhong. CLASSIFICATION OF SOLUTIONS FOR A CLASS OF SINGULAR INTEGRAL SYSTEM[J]. Acta mathematica scientia,Series B, 2011, 31(4): 1449-1456.

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CLASSIFICATION OF SOLUTIONS FOR A CLASS OF SINGULAR INTEGRAL SYSTEM

CLASSIFICATION OF SOLUTIONS FOR A CLASS OF SINGULAR INTEGRAL SYSTEM

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