Singularly perturbed elliptic equations with solutions concentrating on a 1-dimensional orbit
type: Item
instance of: scholarly article
title: Singularly perturbed elliptic equations with solutions concentrating on a 1-dimensional orbit
zbMATH Open document ID: 1189.35103
DOI: 10.4171/JEMS/203
author: Bernhard Ruf
author: P. N. Srikanth
published in: Journal of the European Mathematical Society (JEMS)
publication date: 2010-04-29T00:00:00Z
full work available at URL: http://www.ems-ph.org/journals/journal.php
review text: Summary: We consider a singularly perturbed elliptic equation with superlinear nonlinearity on an annulus in \(\mathbb R^4\), and look for solutions which are invariant under a fixed point free 1-parameter group action. We show that this problem can be reduced to a nonhomogeneous equation on a related annulus in dimension 3. The ground state solutions of this equation are single peak solutions which concentrate near the inner boundary. Transforming back, these solutions produce a family of solutions which concentrate along the orbit of the group action near the inner boundary of the domain.
Mathematics Subject Classification ID: 35J61
Mathematics Subject Classification ID: 35J91
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35B45
zbMATH DE Number: 5702772
zbMATH Keywords: superlinear ellliptic equation
zbMATH Keywords: singular perturbation
zbMATH Keywords: peaked solutions
zbMATH Keywords: concentrating solutions
Wikidata QID: Q59310976
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5702772