SINGULAR CRITICAL ELLIPTIC PROBLEMS WITH FRACTIONAL LAPLACIAN

被引：0

作者：

Wang, Xueqiao ^{[1
]}

Yang, Jianfu ^{[1
]}

机构：

[1] Jiangxi Normal Univ, Dept Math, Nanchang 330022, Jiangxi, Peoples R China

来源：

ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS | 2015年

关键词：

Fractional Laplacian; singular critical problem; non-contractible domain; CRITICAL SOBOLEV; INEQUALITIES; EXISTENCE; CONSTANTS;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we consider the existence of solutions of the critical problem with a Hardy term for fractional Laplacian (-Delta)(s)u - mu u/vertical bar x vertical bar(2s) = u(2)*s(-1) in Omega, u > 0 in Omega, u = 0 on partial derivative Omega, where Omega subset of R-N is a smooth bounded domain and 0 is an element of Omega, mu is a positive parameter, N > 2s and s is an element of (0, 1), 2*(s) = 2N/N-2s is the critical exponent. (-Delta)(s) stands for the spectral fractional Laplacian. Assuming that Omega is non-contractible, we show that there exists mu(0) > 0 such that 0 < mu < mu(0), there exists a solution. We also discuss a similar problem for the restricted fractional Laplacian.

引用

页数：12

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