Singular solutions of a Hénon equation involving a nonlinear gradient term
type: Item
instance of: scholarly article
title: Singular solutions of a Hénon equation involving a nonlinear gradient term
zbMATH Open document ID: 1483.35100
author: Craig Cowan
author: Abdolrahman Razani
published in: Communications on Pure and Applied Analysis
publication date: 2022-01-21T00:00:00Z
review text: This article investigates the existence of positive singular solutions to \(-\Delta u=|x|^\alpha |\nabla u|^p\) in \(\Omega\), subject to the boundary condition \(u=0\) on \(\partial \Omega\). Here \(\Omega\subset \mathbb{R}^N\) is a small smooth perturbation of the unit ball in \(\mathbb{R}^N\), \(\alpha>-1\) and either \((N+\alpha)/(N-1)<p<2+\alpha\) or \(p>2+\alpha\). The main result established the existence of a positive singular solution whose behaviour around the origin is given by a specific radial function. The approach combines linear theory and a fixed point argument on the deformation of the ball.
reviewed by: Marius Ghergu
Mathematics Subject Classification ID: 35J91
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35A01
zbMATH DE Number: 7461703
zbMATH Keywords: semilinear equation with Laplacian
zbMATH Keywords: Dirichlet problem
zbMATH Keywords: existence of singular solutions
MaRDI profile type: Publication
full work available at URL: cpaa.2021172
OpenAlex ID: W3204473462
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DOI: 10.3934/CPAA.2021172
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description: scientific article; zbMATH DE number 7461703