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Volume 18, Issue 2

# The Bahri–Coron Theorem for Fractional Yamabe-Type Problems

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

## Abstract

We study the following fractional Yamabe-type equation:

Here Ω is a regular bounded domain of ${ℝ}^{n}$, $n\ge 2$, and ${A}_{s}$, $s\in \left(0,1\right)$, represents the fractional Laplacian operator ${\left(-\mathrm{\Delta }\right)}^{s}$ 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].

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

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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,

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