Exact solutions of nonlinear conformally invariant integral equations in R3

被引：46

作者：

Xu, XW ^{[1
]}

机构：

[1] Natl Univ Singapore, Dept Math, Singapore 117543, Singapore

来源：

ADVANCES IN MATHEMATICS | 2005年 / 194卷 / 02期

关键词：

exact solution; conformally invariant integral equation; method of moving spheres;

D O I：

10.1016/j.aim.2004.07.004

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we will study the entire positive C-4 solutions of the geometrically interesting integral equation: u(x) = 1/8 pi integral(3)(R) vertical bar x -y vertical bar u(-q)(y)dy with 0 < q in R-3. We will show that there are positive entire solutions which take the form u(x) = c(1+vertical bar x vertical bar(2))(1/2) up to dilation and translations, only when q = 7. (c) 2004 Elsevier Inc. All rights reserved.

引用

页码：485 / 503

页数：19

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