Local behavior and global existence of positive solutions of \(au^\lambda\leq -\Delta u\leq u^\lambda\).
type: Item
instance of: scholarly article
title: Local behavior and global existence of positive solutions of \(au^\lambda\leq -\Delta u\leq u^\lambda\).
zbMATH Open document ID: 1039.35145
DOI: 10.1016/S0294-1449(02)00105-1
author: Steven D. Taliaferro
published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire
publication date: 2002-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/78565
review text: The author deals with the problem \[ au^\lambda\leq -\Delta u\leq u^\lambda \tag{1} \] in various subsets of \(\mathbb{R}^n\), where \(a\in(0,1)\) and \(n>2\). He investigates the behaviour near the origin of \(C^2\) positive solutions \(u(x)\) of (1), in a punctured neighborhood of the origin in \(\mathbb{R}^n\), where \(\frac{n}{n-2} <\lambda< \frac{n+2}{n-2}\). Moreover, he studies the existence of \(C^2\) positive solutions of (1) on \(\mathbb{R}^n\). The author investigates the qualitative behaviour of solutions of (1) depending on the parameter \(a\).
Mathematics Subject Classification ID: 35R45
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35B05
zbMATH DE Number: 1881301
zbMATH Keywords: behaviour near the origin of \(C^2\) positive solutions
zbMATH Keywords: existence of \(C^2\) positive solutions
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
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OpenAlex ID: W1983272323
description: scientific article; zbMATH DE number 1881301