INFINITELY MANY ARBITRARILY SMALL SOLUTIONS FOR SINGULAR ELLIPTIC PROBLEMS WITH CRITICAL SOBOLEV-HARDY EXPONENTS

被引：19
|
作者：
He, Xiaoming [1 ,2 ]
Zou, Wenming [1 ]
机构：
[1] Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China
[2] Cent Univ Nationalities, Dept Math Sci, Beijing 100081, Peoples R China
来源：
PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY | 2009年 / 52卷
基金：
中国博士后科学基金;
关键词：
singular elliptic equation; multiple solutions; critical Sobolev Hardy growth; compactness; MULTIPLE SOLUTIONS; EXISTENCE; EQUATIONS; CONSTANT; LEMMA;
D O I：
10.1017/S0013091506001568
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let Omega subset of R-N be a bounded domain such that 0 is an element of Omega, N >= 3, 2*(s) = 2(N - s) / (N - 2), 0 <= s < 2, 0 <= mu < mu = 1/4(N - 2)(2). We obtain the existence of infinitely many solutions for the singular critical problem Delta u - mu(u / vertical bar x vertical bar(2)) = (vertical bar u vertical bar(2)*((s)-2) / vertical bar x vertical bar(s))u + lambda f (x, u) with Dirichlet boundary condition for suitable positive number lambda.
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页码：97 / 108
页数：12
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