SOME PROPERTIES OF POSITIVE SOLUTIONS FOR AN INTEGRAL SYSTEM WITH THE DOUBLE WEIGHTED RIESZ POTENTIALS

被引：2

作者：

Xu, Jiankai ^{[1
]}

Jiang, Song ^{[2
]}

Wu, Huoxiong ^{[3
]}

机构：

[1] Hunan Agr Univ, Coll Sci, Changsha 410128, Hunan, Peoples R China

[2] Inst Appl Phys & Computat Math, POB 8009, Beijing 100088, Peoples R China

[3] Xiamen Univ, Sch Math Sci, Xiamen 361005, Fujian, Peoples R China

来源：

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

关键词：

Integral system; radially symmetry solution; moving plane method; regularity lifting lemma; weighted-Hardy-Littlewood-Sobolev inequality; ASYMPTOTIC-BEHAVIOR; SYMMETRY;

D O I：

10.3934/cpaa.2016030

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study some important properties of positive solutions for a nonlinear integral system. With the help of the method of moving planes in an integral form, we show that under certain integrable conditions, all of positive solutions to this system are radially symmetric and decreasing with respect to the origin. Meanwhile, using the regularity lifting lemma, which was recently introduced by Chen and Li in [1], we obtain the optimal integrable intervals and sharp asymptotic behaviors for such positive solutions, which characterize the closeness of system to some extent.

引用

页码：2117 / 2134

页数：18

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