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.
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页码：1146 / 1164
页数：19
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