Coincidence points for perturbations of linear Fredholm maps of index zero
type: Item
instance of: scholarly article
title: Coincidence points for perturbations of linear Fredholm maps of index zero
zbMATH Open document ID: 0953.55002
author: Ravi P. Agarwal
author: Donal O'Regan
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 2001-01-29T00:00:00Z
review text: Let \(X\) and \(E\) be Fréchet spaces, \(\operatorname {dom} L\) a vector subspace of \(X\) and \(L: \operatorname {dom} L\to E\) a linear Fredholm map of index zero. For \(U\) an open subset of \(X\) containing 0, let \(G:\overline{U}\to E\) be a continuous map satisfying a technical condition (Mönch-Precup). Hypotheses are presented that imply the existence of a coincidence of \(L\) and \(G\), that is, a solution to the equation \(Lx= G(x)\). Such coincidences correspond, for instance, to solutions to systems of first-order ordinary differential equations. The key requirement is for the existence of an essential map in the sense of \textit{A. Granas} [C. R. Acad. Sci., Paris, Sér A 282, 983-985 (1976; Zbl 0348.47039)] which is combined with homotopy techniques to produce the coincidence. The authors extend their results to the setting of multivalued maps with a view toward applications to differential inclusions.
Mathematics Subject Classification ID: 55M20
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 54H25
Mathematics Subject Classification ID: 47H10
zbMATH DE Number: 1455562
zbMATH Keywords: essential map
zbMATH Keywords: Fréchet spaces
zbMATH Keywords: multivalued maps
reviewed by: Robert F. Brown
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195143420
OpenAlex ID: W2034557223
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DOI: 10.2977/PRIMS/1195143420
description: scientific article; zbMATH DE number 1455562