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

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

Abstract

Abstract:

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.

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

CLC Number:

35J60

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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