INFINITELY MANY SOLUTIONS FOR A SINGULAR ELLIPTIC EQUATION INVOLVING CRITICAL SOBOLEV-HARDY EXPONENTS IN RN

doi:10.1016/S0252-9602(10)60082-3

数学物理学报(英文版) ›› 2010, Vol. 30 ›› Issue (3): 830-840.doi: 10.1016/S0252-9602(10)60082-3

INFINITELY MANY SOLUTIONS FOR A SINGULAR ELLIPTIC EQUATION INVOLVING CRITICAL SOBOLEV-HARDY EXPONENTS IN R^N

贺小明, 邹文明

School of |Sciences, Central University for Nationalities, Beijing 100081, China； Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China

收稿日期:2007-10-09 出版日期:2010-05-20 发布日期:2010-05-20
基金资助:
Supported by NSFC (10971238, 10871109)

INFINITELY MANY SOLUTIONS FOR A SINGULAR ELLIPTIC EQUATION INVOLVING CRITICAL SOBOLEV-HARDY EXPONENTS IN R^N

HE Xiao-Ming, ZOU Wen-Ming

School of |Sciences, Central University for Nationalities, Beijing 100081, China； Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China

Received:2007-10-09 Online:2010-05-20 Published:2010-05-20
Supported by:
Supported by NSFC (10971238, 10871109)

摘要/Abstract

摘要：

In this article, we study the existence of multiple solutions for the singular semilinear elliptic equation involving critical Sobolev-Hardy exponents
-?u-u u/|x|²=α |u|^2*(s)-2u/|x|^s+ βa(x)|u|^r-2 u, x ∈ R^N.
By means of the concentration-compactness principle and minimax methods, we obtain infinitely many solutions which tend to zero for suitable positive parameters α, β.

关键词: Singular elliptic equation, Multiple solutions, Critical Sobolev-Hardy exponent, Minimax method

Abstract:

Key words: Singular elliptic equation, Multiple solutions, Critical Sobolev-Hardy exponent, Minimax method

中图分类号:

35J60

贺小明, 邹文明. INFINITELY MANY SOLUTIONS FOR A SINGULAR ELLIPTIC EQUATION INVOLVING CRITICAL SOBOLEV-HARDY EXPONENTS IN R^N[J]. 数学物理学报(英文版), 2010, 30(3): 830-840.

HE Xiao-Ming, ZOU Wen-Ming. INFINITELY MANY SOLUTIONS FOR A SINGULAR ELLIPTIC EQUATION INVOLVING CRITICAL SOBOLEV-HARDY EXPONENTS IN R^N[J]. Acta mathematica scientia,Series B, 2010, 30(3): 830-840.

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INFINITELY MANY SOLUTIONS FOR A SINGULAR ELLIPTIC EQUATION INVOLVING CRITICAL SOBOLEV-HARDY EXPONENTS IN R^N

INFINITELY MANY SOLUTIONS FOR A SINGULAR ELLIPTIC EQUATION INVOLVING CRITICAL SOBOLEV-HARDY EXPONENTS IN R^N

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