Exact solutions of nonlinear conformally invariant integral equations in R3

被引：48
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.
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收藏
页码：485 / 503
页数：19
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