Classification of solutions for an integral system with negative exponents

被引：6
作者：
Wang, Guanglan [1 ]
Liu, Zhao [2 ]
Chen, Lu [1 ]
机构：
[1] Beijing Normal Univ, Sch Math Sci, Beijing, Peoples R China
[2] Jiangxi Sci & Technol Normal Univ, Sch Math & Comp Sci, Nanchang, Jiangxi, Peoples R China
来源：
COMPLEX VARIABLES AND ELLIPTIC EQUATIONS | 2019年 / 64卷 / 02期
关键词：
Asymptotic behaviour; classification of solutions; conformal invariant; method of moving spheres; regularity; POSITIVE SOLUTIONS; EQUATIONS; UNIQUENESS; SYMMETRY; THEOREMS;
D O I：
10.1080/17476933.2018.1427079
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we study the following integral system with negative exponents {u(x) = integral(Rn) vertical bar x-y vertical bar(nu 1)f(u,v)(y)dy, v(x) = integral(Rn) vertical bar x-y vertical bar(nu 2)g(u,v)(y)dy, where f(u,v) = lambda(1)u(-p1) + mu(1)v(-q1) + gamma(1)u(-alpha)v(-beta), g(u,v) = lambda(2)u(-p2) + mu(2)v(-q2) + gamma(2)u(-beta)v(-alpha). We obtain asymptotic behaviour and regularity for positive solutions, and in the critical case, we classify all of them by applying the method of moving spheres. We also consider weighted integral systems with negative exponents and derive asymptotic behaviours for positive solutions.
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页码：204 / 222
页数：19
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