Exact singular behavior of positive solutions to nonlinear elliptic equations with a Hardy potential
type: Item
instance of: scholarly article
title: Exact singular behavior of positive solutions to nonlinear elliptic equations with a Hardy potential
zbMATH Open document ID: 1372.35107
author: Lei Wei
author: Yihong Du
published in: Journal of Differential Equations
publication date: 2017-01-26T00:00:00Z
review text: The authors study the singular behaviour at \(x=0\) of positive solutions to the problem \[ -\Delta u=\frac{\lambda}{|x|^2}u-|x|^\sigma u^p,\;\;x\in \Omega\setminus \{0\}, \] where \(\Omega\) is a bounded smooth domain of \(\mathbb{R}^N\) containing the origin, and \(p>1\), \(\sigma >-2\) are constants. If \(\lambda \leq (N-2)^2/4\), the behaviour at the origin of all positive solutions has recently been classified, and includes subcases where \(u\) converges and blows-up as \(x\to 0\). In the paper under review, it is shown that if \(\lambda > (N-2)^2/4\) then all positive solutions blow-up at the origin with the same rate, which is given explicitly.
reviewed by: Christos Sourdis
Mathematics Subject Classification ID: 35J61
Mathematics Subject Classification ID: 35J75
zbMATH DE Number: 6678280
zbMATH Keywords: Hardy potential
zbMATH Keywords: isolated singularity
zbMATH Keywords: positive solution
MaRDI profile type: Publication
full work available at URL: j.jde.2016.12.004
OpenAlex ID: W2565836089
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DOI: 10.1016/J.JDE.2016.12.004
description: scientific article; zbMATH DE number 6678280