Index bundle, Leray-Schauder reduction and bifurcation of solutions of nonlinear elliptic boundary value problems.
type: Item
instance of: scholarly article
title: Index bundle, Leray-Schauder reduction and bifurcation of solutions of nonlinear elliptic boundary value problems.
zbMATH Open document ID: 1033.58021
DOI: 10.12775/TMNA.2001.033
author: Jacobo Pejsachowicz
published in: Topological Methods in Nonlinear Analysis
publication date: 2001-01-01T00:00:00Z
review text: The main result of the paper is the following: A family \(\{F_p:p \in P\}\) of elliptic boundary value problems of index \(0\) parametrized by a compact manifold admits a reduction to a family of compact vector fields parametrized by \(P\) if and only if its index bundle \(\text{Ind}\,F\) vanishes. Next the author describes the restriction on the degree of the map \(F_p\) imposed by non vanishing of the image of \(\text{Ind}\,F\) under the generalized \(J\)-homeomorphism. From this the author obtains a number of corollaries about bifurcation from infinity for solutions of nonlinear elliptic boundary value problems.
Mathematics Subject Classification ID: 58J20
Mathematics Subject Classification ID: 58J55
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 47J15
Mathematics Subject Classification ID: 54H25
zbMATH DE Number: 1799622
zbMATH Keywords: index bundle
zbMATH Keywords: bifurcation
zbMATH Keywords: nonlinear elliptic boundary value problems
reviewed by: Jarosław Górnicki
MaRDI profile type: Publication
full work available at URL: tmna.2001.033
OpenAlex ID: W57267810
description: scientific article; zbMATH DE number 1799622