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.

引用

页码：2586 / 2594

页数：9

共 19 条

[1] ASYMPTOTIC SYMMETRY AND LOCAL BEHAVIOR OF SEMILINEAR ELLIPTIC-EQUATIONS WITH CRITICAL SOBOLEV GROWTH [J].