A Morse lemma at infinity for nonlinear elliptic fractional equations
type: Item
instance of: scholarly article
title: A Morse lemma at infinity for nonlinear elliptic fractional equations
zbMATH Open document ID: 1484.35211
DOI: 10.4171/RSMUP/82
author: Wael Abdelhedi
author: Zeinab Mhamdi
author: H. Hajaiej
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 2022-02-14T00:00:00Z
review text: Summary: In this paper, we consider the nonlinear fractional critical equation with zero Dirichlet boundary condition \(A_s u= K u^{\frac{n+2s}{n-2s}}\), \(u>0\) in \(\Omega\) and \(u=0\) on \(\partial\Omega\), where \(K\) is a positive function, \(\Omega\) is a regular bounded domain of \(\mathbb{R}^n\), \(n\geq 2\) and \(A_s\), \(s\in (0,1)\) represents the spectral fractional Laplacian operator \((-\Delta)^s\) in \(\Omega\) with zero Dirichlet boundary condition. We prove a version of Morse lemmas at infinity for this problem. We also exhibit a relevant application of our novel result. More precisely, we characterize the critical points at infinity of the associated variational problem and we prove an existence result for \(s=\frac{1}{2}\) and \(n=3\).
Mathematics Subject Classification ID: 35J61
Mathematics Subject Classification ID: 35R11
Mathematics Subject Classification ID: 35J67
zbMATH DE Number: 7473027
zbMATH Keywords: semilinear equation with fractional Laplacian
zbMATH Keywords: Dirichlet problem
zbMATH Keywords: Morse lemma
Wikidata QID: Q114021363
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.4171/rsmup/82
OpenAlex ID: W3165826934
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description: scientific article; zbMATH DE number 7473027