Exponential dichotomies for solitary-wave solutions of semilinear elliptic equations on infinite cylinders
type: Item
instance of: scholarly article
title: Exponential dichotomies for solitary-wave solutions of semilinear elliptic equations on infinite cylinders
zbMATH Open document ID: 0908.35048
author: Daniela Peterhof
author: Arnd Scheel
author: B. Sandstede
published in: Journal of Differential Equations
publication date: 1999-03-23T00:00:00Z
review text: The authors investigate the elliptic equation \[ u_{xx}+ \Delta_yu+ g(y,u,u_x,\nabla_y u)= 0,\quad (x,y)\in \mathbb{R}\times\Omega\tag{1} \] in the infinite cylinders \(\mathbb{R}\times \Omega\), where \(\Omega\) is an open and bounded subset in \(\mathbb{R}^n\) with boundary conditions prescribed on \(\mathbb{R}\times \partial\Omega\). The main idea of the paper is to consider problem (1) as a dynamical system with respect to \(x\). In terms of this idea, results on stability and continuity of the exponential dichotomy for problem (1) are obtained. The presentation is supplied with an example.
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 35B32
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 1109521
zbMATH Keywords: dynamical system treatment of elliptic equations
reviewed by: A. A. Martynyuk
MaRDI profile type: Publication
OpenAlex ID: W2084202510
Wikidata QID: Q60143943
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DOI: 10.1006/JDEQ.1997.3303
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description: scientific article; zbMATH DE number 1109521