On the fractional Lazer-McKenna conjecture with superlinear potential
type: Item
instance of: scholarly article
title: On the fractional Lazer-McKenna conjecture with superlinear potential
zbMATH Open document ID: 1403.35311
author: A. Dieb
author: Fethi Mahmoudi
author: Boumediene Abdellaoui
published in: Calculus of Variations and Partial Differential Equations
publication date: 2018-12-10T00:00:00Z
review text: The authors study superlinear problems involving the fractional Laplace operator \[ (-\Delta)^s u =|u|^{p} -\sigma\phi_1 \text{ in } \Omega, \text{ with } u >0 \text{ in } \Omega, \text{ and } u=0 \text{ in } \mathbb{R}^N\setminus\Omega \] where \(0<s<1\), \(1<p < \frac{N+2s}{N-2s}\), \(\Omega\) is a domain in \(\mathbb{R}^N\) with Lipschitz boundary, and \(\phi_1\) is the first positive eigenfunction of the fractional Laplacian with Dirichlet boundary conditions. By a Lyapunov-Schmidt reduction technique, as \(\sigma\) increases indefinitely, more and more multi-peaked solutions with peaks concentrated near local maximum points of \(\phi_1\) are obtained.
reviewed by: Florin Catrina
Mathematics Subject Classification ID: 35R11
Mathematics Subject Classification ID: 35A15
Mathematics Subject Classification ID: 35A16
Mathematics Subject Classification ID: 35J61
zbMATH DE Number: 6991666
zbMATH Keywords: fractional Laplacian
zbMATH Keywords: superlinear problem
zbMATH Keywords: multiplicity of solutions
zbMATH Keywords: Lyapunov-Schmidt reduction
MaRDI profile type: Publication
full work available at URL: s00526-018-1444-5
OpenAlex ID: W2902418176
Wikidata QID: Q123113132
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DOI: 10.1007/S00526-018-1444-5
description: scientific article; zbMATH DE number 6991666