INFINITELY MANY SIGN-CHANGING SOLUTIONS FOR THE BRZIS-NIRENBERG PROBLEM INVOLVING HARDY POTENTIAL 被引量：3

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

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摘要 In this article, we give a new proof on the existence of infinitely many sign- changing solutions for the following Brezis-Nirenberg problem with critical exponent and a Hardy potential -△u-μ（u/｜x｜^2）=λu＋｜u｜^2＊-2u inΩ, u=0 on eΩ,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 Lj usternik-Schnirelman theory. In this article, we give a new proof on the existence of infinitely many sign- changing solutions for the following Brezis-Nirenberg problem with critical exponent and a Hardy potential -△u-μ（u/｜x｜^2）=λu＋｜u｜^2＊-2u inΩ, u=0 on eΩ,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 Lj usternik-Schnirelman theory.

作者张靖马世旺

机构地区 Mathematics Science College School of Mathematical Sciences and LPMC

出处《Acta Mathematica Scientia》 SCIE CSCD 2016年第2期527-536,共10页 数学物理学报（B辑英文版）

基金 supported by the Specialized Fund for the Doctoral Program of Higher Education and the National Natural Science Foundation of China

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

分类号 O175 [理学—基础数学]

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1Ambrosetti A, Rabinowitz P H. Dual variational methods in critical point theory and applications. J FunCt Anal, 1973, 14:349-381.
2Atkinson F V, Brezis H, Peletier L A. Nodal solutions of elliptic equations with critical Sobolev exponents. J Differential Equations, 1997, 134:1-25.
3Bartsch T, Liu Z, Weth T. Sign changing solutions of superlinear SchrSdinger equations. Commun Partial Differential Equations, 2004, 29:25-42.
4Bartsch T, Liu Z, Weth T. Nodal solutions of a p-Laplcain equation. Proc London Math Soc, 2005, 91: 129-152.
5Cao D, Han P. Solutions for semilinear elliptic equations with critical exponents and Hardy potential. J Differential Equations, 2004, 205:521-537.
6Cao D, Peng S. A note on the sign-changing solutions to elliptic problems with critical Sobolev and Hardy terms. J Differential Equations, 2003, 193:424-434.
7Cao D, Yan S. Infinitely many solutions for an elliptic problem involving critical Sobolev growth and Hardy potential. Calc Var Partial Differnential Equations, 2010, 38:471-501.
8Cao D, Peng S, Yan S. Infinitely many solutions for p-Laplacian equation involving critical Sobolev growth. J Funct Anal, 2012, 262:2861-2902.
9Chen Z, Zou W. On an elliptic problem with critical exponent and Hardy potential. J Differential Equations, 2012, 252:969-987.
10Devillanova G, Solomini S. Concentration estimates and multiple solutions to elliptic problems at critical growth. Adv Differ Equ, 2002, 7:1257-1280.