INFINITELY MANY SIGN-CHANGING SOLUTIONS FOR THE BREZIS-NIRENBERG PROBLEM INVOLVING THE FRACTIONAL LAPLACIAN

被引：12

作者：

Li, Lin ^{[1
]}

Sun, Jijiang ^{[2
]}

Tersian, Stepan ^{[3
,4
]}

机构：

[1] Chongqing Technol & Business Univ, Sch Math & Stat, Chongqing 400067, Peoples R China

[2] Nanchang Univ, Dept Math, Nanchang 330031, Jiangxi, Peoples R China

[3] Univ Ruse, Dept Math, Ruse 7017, Bulgaria

[4] Bulgarian Acad Sci, Inst Math & Informat, Sofia 1113, Bulgaria

来源：

FRACTIONAL CALCULUS AND APPLIED ANALYSIS | 2017年 / 20卷 / 05期

基金：

中国国家自然科学基金;

关键词：

fractional critical exponent; sign-changing solutions; invariant sets; minimax method; NONLINEAR ELLIPTIC PROBLEMS; CRITICAL SOBOLEV EXPONENTS; MULTIPLE SOLUTIONS; SCHRODINGER-EQUATIONS; OBSTACLE PROBLEM; BOUNDARY; OPERATOR; COMPACTNESS; REGULARITY; EXISTENCE;

D O I：

10.1515/fca-2017-0061

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider the following Brezis-Nirenberg problem involving the fractional Laplacian operator: {(-Delta)(s)u = lambda u + vertical bar u vertical bar(2s)* (- 2)u in Omega, u = 0 on partial derivative Omega, where s is an element of (0, 1), Omega is a bounded smooth domain of R-N (N > 6s) and 2(s)* = 2N/N-2s is the critical fractional Sobolev exponent. We show that, for each lambda > 0, this problem has infinitely many sign-changing solutions by using a compactness result obtained in [34] and a combination of invariant sets method and Ljusternik-Schnirelman type minimax method.

引用

页码：1146 / 1164

页数：19

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