Singular boundary value problems via the Conley index
type: Item
instance of: scholarly article
title: Singular boundary value problems via the Conley index
zbMATH Open document ID: 1154.34011
author: Tomáš Gedeon
author: K. Mischaikow
published in: Topological Methods in Nonlinear Analysis
publication date: 2008-01-02T00:00:00Z
review text: The authors consider a singular system of the form \[ \varepsilon^2 D u'' + f(t,u,\varepsilon u')=0 \] with \(u(t) \in {\mathbb R}^n\) and \(D\) a diagonal matrix, together with boundary conditions which generalize linear boundary conditions of Sturm-Liouville type. For the main result it is assumed that in case \(\varepsilon =0\) there exist two hyperbolic saddle points, and hypotheses are made on the corresponding stable/unstable manifolds. Thus, an existence result is given for \(\varepsilon\) sufficiently small. The proof is performed in the framework of Conley index theory. An interesting feature of this paper is that Conley index theory is used for establishing solutions to a boundary value problem and not (what is more standard) for detecting the existence of invariant sets.
reviewed by: Anna Capietto
Mathematics Subject Classification ID: 34B16
Mathematics Subject Classification ID: 55N45
Mathematics Subject Classification ID: 34D15
zbMATH DE Number: 5222350
zbMATH Keywords: singular boundary value problems
zbMATH Keywords: Conley index
MaRDI profile type: Publication
description: scientific article