Mixed states for an Allen-Cahn type equation. II
type: Item
instance of: scholarly article
title: Mixed states for an Allen-Cahn type equation. II
zbMATH Open document ID: 1161.35397
author: Paul H. Rabinowitz
author: E. Stredulinsky
published in: Calculus of Variations and Partial Differential Equations
publication date: 2004-11-05T00:00:00Z
review text: The authors deal with the existence of multibump solutions for an Allen-Cahn equation: \[ -\Delta u+F_u'(x,y,u)=0,\tag{1} \] where \((x,y) \in\mathbb R^2\) and \(F\) is a given function. Under some suitable assumptions on \(F\), that is, by eliminating a strong spatial reversibility condition and by weakining certain nondegeneracy conditions on families of basic heteroclinic solutions, the authors using novel minimization arguments establish the existence of multibump solutions.
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 58E30
Mathematics Subject Classification ID: 47J30
Mathematics Subject Classification ID: 35J20
zbMATH DE Number: 2113881
zbMATH Keywords: multibump solutions
zbMATH Keywords: minimization
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: s00526-003-0251-8
OpenAlex ID: W1970721684
DOI: 10.1007/S00526-003-0251-8
description: scientific article; zbMATH DE number 2113881