ASYMPTOTIC BEHAVIOR FOR SOLUTIONS OF SOME INTEGRAL EQUATIONS

被引：27

作者：

Lei, Yutian ^{[1
]}

Ma, Chao ^{[2
]}

机构：

[1] Nanjing Normal Univ, Sch Math Sci, Nanjing 210097, Peoples R China

[2] Univ Colorado, Dept Math, Boulder, CO 80309 USA

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2011年 / 10卷 / 01期

关键词：

Integral equations; asymptotic analysis; singularities; weighted Hardy-Littlewood-Sobolev inequality; NONLINEAR ELLIPTIC-EQUATIONS; HARDY-LITTLEWOOD-SOBOLEV; SYSTEM; SYMMETRY; CLASSIFICATION;

D O I：

10.3934/cpaa.2011.10.193

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study the asymptotic behavior of the positive solutions of the following system of Euler-Lagrange equations of the Hardy-Littlewood-Sobolev type in R(n) u(x) = 1/vertical bar x vertical bar(alpha) integral(Rn) v(y)(q)/vertical bar y vertical bar(beta)vertical bar x - y vertical bar(lambda) dy, v(x) = 1/vertical bar x vertical bar(beta) integral(Rn) u(y)(p)/vertical bar y vertical bar(alpha)vertical bar x - y vertical bar(lambda) dy. We obtain the growth rate of the solutions around the origin and the decay rate near infinity. Some new cases beyond the work of C. Li and J. Lim [17] are studied here. In particular, we remove some technical restrictions of [17], and thus complete the study of the asymptotic behavior of the solutions for non-negativ alpha and beta.

引用

页码：193 / 207

页数：15

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