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Advanced Nonlinear Studies

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Volume 18, Issue 2


The Bahri–Coron Theorem for Fractional Yamabe-Type Problems

Wael Abdelhedi / Hichem Chtioui / Hichem Hajaiej
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  • Department of Mathematics, California State University, 5151 State University Drive, Los Angeles, CA 90032-8204, USA
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Published Online: 2017-11-04 | DOI: https://doi.org/10.1515/ans-2017-6035


We study the following fractional Yamabe-type equation:

{Asu=un+2sn-2s,u>0in Ω,u=0on Ω,

Here Ω is a regular bounded domain of n, n2, and As, s(0,1), represents the fractional Laplacian operator (-Δ)s in Ω with zero Dirichlet boundary condition. We investigate the effect of the topology of Ω on the existence of solutions. Our result can be seen as the fractional counterpart of the Bahri–Coron theorem [3].

Keywords: Fractional PDE; Variational Method; Critical Exponent; Loss of Compactness

MSC 2010: 35J65; 35R11; 58J20; 58C30


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About the article

Received: 2017-06-04

Revised: 2017-10-01

Accepted: 2017-10-04

Published Online: 2017-11-04

Published in Print: 2018-04-01

Citation Information: Advanced Nonlinear Studies, Volume 18, Issue 2, Pages 393–407, ISSN (Online) 2169-0375, ISSN (Print) 1536-1365, DOI: https://doi.org/10.1515/ans-2017-6035.

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