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.

引用

页码：97 / 108

页数：12

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