Liouville type theorems for the system of integral equations

被引：12
|
作者：
Dou, Jingbo [1 ,2 ]
机构：
[1] Xian Univ Finance & Econ, Sch Stat, Xian 710100, Shaanxi, Peoples R China
[2] NW Univ Xian, Ctr Nonlinear Studies, Xian 710069, Shaanxi, Peoples R China
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2010年 / 217卷 / 06期
基金：
中国国家自然科学基金;
关键词：
Hardy-Littlewood-Sobolev inequality; System of integral equations; Moving spheres method; Conformal invariance; Liouville type theorem; SEMILINEAR ELLIPTIC-EQUATIONS; HARDY-LITTLEWOOD-SOBOLEV; MOVING SPHERES; ASYMPTOTIC SYMMETRY; CRITICAL EXPONENTS; POSITIVE SOLUTIONS; R-N; CLASSIFICATION; INEQUALITIES; UNIQUENESS;
D O I：
10.1016/j.amc.2010.07.071
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Consider the system of integral equations in R(n) {u(x) - integral(Rn) vertical bar x-y vertical bar(a-n)u(y)(p)v(y)(q)dy, v(x) = integral(Rn) vertical bar x-y vertical bar(a-n)u(y)(q)v(y)(p)dy, where 0 < alpha < n; 1 <= p; q <= n+alpha/n-alpha. Its positive solutions are classified by developing the method of moving spheres with p+q = n+alpha/n-alpha. When p+q < n+alpha/n-alpha the nonexistence of any positive solutions is also discussed. (C) 2010 Elsevier Inc. All rights reserved.
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页码：2586 / 2594
页数：9
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