Classification of the solutions of semilinear elliptic problems in a ball
type: Item
instance of: scholarly article
title: Classification of the solutions of semilinear elliptic problems in a ball
zbMATH Open document ID: 0968.35042
author: Rafael D. Benguria
author: Jean Dolbeault
author: Maria J. Esteban
published in: Journal of Differential Equations
publication date: 2000-12-19T00:00:00Z
full work available at URL: http://hdl.handle.net/10533/172101
review text: This paper fully describes the set of the positive and nodal (regular and singular) radial solutions of the superlinear elliptic problem: \[ -\Delta u=\lambda u+|u|^{p-1} u\quad\text{in }B,\qquad u= 0\quad\text{on }\partial B, \] where \(p>1\) and \(B= \{x\in \mathbb{R}^N:|x|< 1\}\). The solutions are of three different types: bounded with a finite number of zeros in \((0,1)\), singular at the origin with a finite number of zeros, and singular with sign changing oscillations at the origin.
reviewed by: Shigeru Sakaguchi
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35B05
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 1545274
zbMATH Keywords: radial solution
zbMATH Keywords: singular solution
zbMATH Keywords: oscillatory solution
zbMATH Keywords: nodal solution
MaRDI profile type: Publication
OpenAlex ID: W2081534539
Wikidata QID: Q59158186
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DOI: 10.1006/JDEQ.2000.3792
description: scientific article; zbMATH DE number 1545274