The Bahri-Coron Theorem for Fractional Yamabe-Type Problems

被引：16

作者：

Abdelhedi, Wael ^{[1
]}

Chtioui, Hichem ^{[1
]}

Hajaiej, Hichem ^{[2
]}

机构：

[1] Fac Sci Sfax, Dept Math, Sfax 3018, Tunisia

[2] Calif State Univ Los Angeles, Dept Math, 5151 State Univ Dr, Los Angeles, CA 90032 USA

来源：

ADVANCED NONLINEAR STUDIES | 2018年 / 18卷 / 02期

关键词：

Fractional PDE; Variational Method; Critical Exponent; Loss of Compactness; EXTENSION PROBLEM; ELLIPTIC PROBLEM; MOVING SPHERES; EQUATIONS; DERIVATIVES; INEQUALITY; LAPLACIAN; EXPONENT;

D O I：

10.1515/ans-2017-6035

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the following fractional Yamabe-type equation: {A(s)u = u (n+2s/n-2s), u > 0 in Omega, u = on partial derivative Omega, Here Omega is a regular bounded domain of R-n, n >= 2, and A(s), s is an element of(0, 1), represents the fractional Laplacian operator (-Delta)(s) in Omega with zero Dirichlet boundary condition. We investigate the effect of the topology of Omega on the existence of solutions. Our result can be seen as the fractional counterpart of the Bahri-Coron theorem[3].

引用

页码：393 / 407

页数：15

共 19 条

[1] ON A NONLINEAR ELLIPTIC EQUATION INVOLVING THE CRITICAL SOBOLEV EXPONENT - THE EFFECT OF THE TOPOLOGY OF THE DOMAIN [J].