A phase plane analysis of the ``multi-bubbling'' phenomenon in some slightly supercritical equations
type: Item
instance of: scholarly article
title: A phase plane analysis of the ``multi-bubbling'' phenomenon in some slightly supercritical equations
zbMATH Open document ID: 1136.35376
author: Jean Dolbeault
author: Monica Musso
author: Manuel del Pino
published in: Monatshefte für Mathematik
publication date: 2004-10-28T00:00:00Z
full work available at URL: https://basepub.dauphine.fr/handle/123456789/6136
review text: The authors deal with the Brezis-Nirenberg problem: \[ \Delta u+|u|^{p-1}u+\lambda u=0,\text{ in }\mathbb B\quad u=0,\text{ on } \partial\mathbb B,\tag{1} \] where \(\mathbb B\) is the unit ball in \(\mathbb R^N\), \(N\geq 3\), \(p^*=\frac{N+2}{N-2}\). The authors are interested in describing the solutions in the slightly supercritical regime: \(p=p^*+\varepsilon\). To this end, the authors perform a phase plane analysis, which emphasize the common heuristic properties of the Brezis-Nirenberg problem in dimension \(N\geq 3\) and an equation involving the exponential nonlinearity in dimension \(N\geq 2\).
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35B25
Mathematics Subject Classification ID: 35P30
Mathematics Subject Classification ID: 34C23
zbMATH DE Number: 2111474
zbMATH Keywords: supercritial problem
zbMATH Keywords: Gelfand problem
zbMATH Keywords: Brezis-Nirenberg problem
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
OpenAlex ID: W4239950652
DOI: 10.1007/S00605-004-0236-5
description: scientific article; zbMATH DE number 2111474