Multi-peak solutions for super-critical elliptic problems in domains with small holes
type: Item
instance of: scholarly article
title: Multi-peak solutions for super-critical elliptic problems in domains with small holes
zbMATH Open document ID: 1014.35028
author: Monica Musso
author: Manuel del Pino
author: P. Felmer
published in: Journal of Differential Equations
publication date: 2002-09-08T00:00:00Z
review text: This paper is devoted to the construction of solutions of the problem \[ \begin{cases} -\Delta u=u^{{N+2 \over N-2}+\varepsilon} \quad &\text{in } \Omega,\\ u>0\quad &\text{in }\Omega,\\ u=0 \quad &\text{on }\partial\Omega, \end{cases}\tag{1} \] where \(\Omega\) is a bounded domain with smooth boundary in \(\mathbb{R}^N\), \(N\geq 3\), and \(\varepsilon >0\) is a small parameter. The goal of this paper is to raise the issue of solvability (1) in a domain exhibiting multiple holes. The main result of the authors states that in such a situation, multi-peak solutions exist, consisting of the glueing of double-spikes associated with each of the holes.
Mathematics Subject Classification ID: 35J60
zbMATH DE Number: 1797571
zbMATH Keywords: multiple holes
zbMATH Keywords: multi-peak solutions
zbMATH Keywords: positive solution
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
OpenAlex ID: W2035234559
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DOI: 10.1006/JDEQ.2001.4098
description: scientific article; zbMATH DE number 1797571