INFINITELY MANY SIGN-CHANGING SOLUTIONS FOR THE BRÉZIS-NIRENBERG PROBLEM INVOLVING HARDY POTENTIAL

doi:10.1016/S0252-9602(16)30018-2

数学物理学报(英文版) ›› 2016, Vol. 36 ›› Issue (2): 527-536.doi: 10.1016/S0252-9602(16)30018-2

INFINITELY MANY SIGN-CHANGING SOLUTIONS FOR THE BRÉZIS-NIRENBERG PROBLEM INVOLVING HARDY POTENTIAL

张靖¹, 马世旺²

1. Mathematics Science College, Inner Mongolia Normal University, Hohhot 010022, China;
2. School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China

收稿日期:2014-10-30 修回日期:2015-10-22 出版日期:2016-04-25 发布日期:2016-04-25
作者简介:Jing ZHANG,E-mail:jinshizhangjing@eyou.com;Shiwang MA,E-mail:shiwangm@163.net
基金资助:
Research supported by the Specialized Fund for the Doctoral Program of Higher Education and the National Natural Science Foundation of China.

INFINITELY MANY SIGN-CHANGING SOLUTIONS FOR THE BRÉZIS-NIRENBERG PROBLEM INVOLVING HARDY POTENTIAL

Jing ZHANG¹, Shiwang MA²

1. Mathematics Science College, Inner Mongolia Normal University, Hohhot 010022, China;
2. School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China

Received:2014-10-30 Revised:2015-10-22 Online:2016-04-25 Published:2016-04-25
Supported by:
Research supported by the Specialized Fund for the Doctoral Program of Higher Education and the National Natural Science Foundation of China.

摘要/Abstract

摘要：

In this article, we give a new proof on the existence of infinitely many sign-changing solutions for the following Brézis-Nirenberg problem with critical exponent and a Hardy potential -Δu-μu/|x|²=λu+|u|^2*-2u in Ω, u=0 on ∂Ω, where Ω is a smooth open bounded domain of R^N which contains the origin, 2^*=2N/N-2 is the critical Sobolev exponent. More precisely, under the assumptions that N≥7, μ∈[0, μ-4), and μ=(N-2)²/4, we show that the problem admits infinitely many sign-changing solutions for each fixed λ>0. Our proof is based on a combination of invariant sets method and Ljusternik-Schnirelman theory.

关键词: Critical exponent, sign-changing solutions, minimax method, hardy potential

Abstract:

Key words: Critical exponent, sign-changing solutions, minimax method, hardy potential

中图分类号:

35J60

张靖, 马世旺. INFINITELY MANY SIGN-CHANGING SOLUTIONS FOR THE BRÉZIS-NIRENBERG PROBLEM INVOLVING HARDY POTENTIAL[J]. 数学物理学报(英文版), 2016, 36(2): 527-536.

Jing ZHANG, Shiwang MA. INFINITELY MANY SIGN-CHANGING SOLUTIONS FOR THE BRÉZIS-NIRENBERG PROBLEM INVOLVING HARDY POTENTIAL[J]. Acta mathematica scientia,Series B, 2016, 36(2): 527-536.

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INFINITELY MANY SIGN-CHANGING SOLUTIONS FOR THE BRÉZIS-NIRENBERG PROBLEM INVOLVING HARDY POTENTIAL

INFINITELY MANY SIGN-CHANGING SOLUTIONS FOR THE BRÉZIS-NIRENBERG PROBLEM INVOLVING HARDY POTENTIAL

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