REGULARITY AND SYMMETRY OF SOLUTIONS OF AN INTEGRAL SYSTEM

doi:10.1016/S0252-9602(12)60139-8

数学物理学报(英文版) ›› 2012, Vol. 32 ›› Issue (5): 1759-1780.doi: 10.1016/S0252-9602(12)60139-8

REGULARITY AND SYMMETRY OF SOLUTIONS OF AN INTEGRAL SYSTEM

陈晓莉^1,2|杨健夫^2*

1. Department of Mathematics, Zhejiang University, Hangzhou 310027, China；
2. Department of Mathematics, Jiangxi Normal University, Nanchang 330022, China

收稿日期:2011-07-04 修回日期:2011-10-08 出版日期:2012-09-20 发布日期:2012-09-20
通讯作者: 杨健夫，jfyang 2000@yahoo.com E-mail:littleli chen@163.com; jfyang 2000@yahoo.com
基金资助:
Chen research is supported by NSF of China (10961015) and Yang research is supported by NSF of China (10961016); the GAN PO555 Program of Jiangxi.

REGULARITY AND SYMMETRY OF SOLUTIONS OF AN INTEGRAL SYSTEM

CHEN Xiao-Li^1,2, YANG Jian-Fu^2*

1. Department of Mathematics, Zhejiang University, Hangzhou 310027, China；
2. Department of Mathematics, Jiangxi Normal University, Nanchang 330022, China

Received:2011-07-04 Revised:2011-10-08 Online:2012-09-20 Published:2012-09-20
Contact: YANG Jian-Fu，jfyang 2000@yahoo.com E-mail:littleli chen@163.com; jfyang 2000@yahoo.com
Supported by:
Chen research is supported by NSF of China (10961015) and Yang research is supported by NSF of China (10961016); the GAN PO555 Program of Jiangxi.

摘要/Abstract

摘要：

In this paper, we are concerned with the regularity and symmetry of positive solutions of the following nonlinear integral system
u(x) = ∫_RⁿG (x − y)v(y)^q/|y| dy, v(x) = ∫_RⁿG (x − y)u(y)^p/|y| dy
for x ∈ Rⁿ, where G (x) is the kernel of Bessel potential of order α, 0 ≤β < α< n, 1 < p, q < n− β/β and 1 /p + 1+1/q + 1>n −α + β/n.
We show that positive solution pairs (u, v) ∈ L^p⁺¹(Rⁿ)×L^q⁺¹(Rⁿ) are H¨older continuous, radially symmetric and strictly decreasing about the origin.

关键词: regularity, radially symmetry, Bessel kernel, nonlinear integral system

Abstract:

Key words: regularity, radially symmetry, Bessel kernel, nonlinear integral system

中图分类号:

35J25

陈晓莉, 杨健夫. REGULARITY AND SYMMETRY OF SOLUTIONS OF AN INTEGRAL SYSTEM[J]. 数学物理学报(英文版), 2012, 32(5): 1759-1780.

CHEN Xiao-Li, YANG Jian-Fu. REGULARITY AND SYMMETRY OF SOLUTIONS OF AN INTEGRAL SYSTEM[J]. Acta mathematica scientia,Series B, 2012, 32(5): 1759-1780.

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REGULARITY AND SYMMETRY OF SOLUTIONS OF AN INTEGRAL SYSTEM

REGULARITY AND SYMMETRY OF SOLUTIONS OF AN INTEGRAL SYSTEM

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