A Leray-Schauder alternative for Mönch maps on closed subsets of Fréchet spaces
type: Item
instance of: scholarly article
title: A Leray-Schauder alternative for Mönch maps on closed subsets of Fréchet spaces
zbMATH Open document ID: 1010.47035
DOI: 10.4171/ZAA/1106
author: Donal O'Regan
author: Marlène Frigon
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 2003-05-18T00:00:00Z
review text: The authors obtain an analogue of the famous Mönch fixed point theorem for maps defined on a closed convex subset of a quasicomplete, metrizable locally convex space which may have an empty interior, as well as a fixed point result of Leray-Schauder type in such a space. The presented results are illustrated by an existence result for first order systems of differential equations \[ y'(t)=g\bigl(t,y(t)\bigr),\quad t\in[0,T] \] \[ y(0)=a=(a_1,a_2,\dots)\in B=\prod_{n\in \mathbb{N}}B_n, \] where \([0,T]\) is a compact interval in \(\mathbb{R}\) and \((B_n,\|\cdot\|_n)\) is a Banach space for every \(n\in\mathbb{N}\). The right-hand side of the above problem satisfies a certain growth condition and a Mönch type condition formulated in terms of a certain measure of noncompactness.
reviewed by: Dariusz Bugajewski
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 34G20
zbMATH DE Number: 1827609
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1827609