Existence and symmetry of positive solutions of an integral equation system

被引：4

作者：

Huang, Xiaotao ^{[1
]}

Li, Dongsheng ^{[1
]}

Wang, Lihe ^{[1
,2
]}

机构：

[1] Xi An Jiao Tong Univ, Coll Sci, Xian 710049, Peoples R China

[2] Univ Iowa, Dept Math, Iowa City, IA 52242 USA

来源：

MATHEMATICAL AND COMPUTER MODELLING | 2010年 / 52卷 / 5-6期

关键词：

Moving spheres; Moving planes; System of integral equations; Symmetry and monotonicity; SEMILINEAR ELLIPTIC-EQUATIONS; FULLY NONLINEAR EQUATIONS; MOVING SPHERES; CLASSIFICATION; INEQUALITIES; THEOREMS; SOBOLEV; HARNACK;

D O I：

10.1016/j.mcm.2010.05.020

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

In this paper, we investigate positive solutions of the following integral equation system in R(n) : {u(x) = integral(Rn) vertical bar x - y vertical bar(alpha-n) v(y)(p)dy, v(x) = integral(Rn) vertical bar x - y vertical bar(beta-n) u(y)(q)dy, where p, q > 1, 0 < alpha, beta < n. With the method of moving spheres, we show the existence and the exact form of its solution in the case p <= (n + alpha)/(n - beta), q <= (n + beta/(n - alpha); and with the method of moving planes, we prove the symmetry and monotonicity of its solution in the case 1/p+1 + 1/q+1 = n-alpha/2n+beta-alpha + n-beta/2n+alpha-beta. (C) 2010 Elsevier Ltd. All rights reserved.

引用

页码：892 / 901

页数：10

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