Aronszajn type theorems for an mth order differential equation in Banach spaces
type: Item
instance of: scholarly article
title: Aronszajn type theorems for an mth order differential equation in Banach spaces
zbMATH Open document ID: 0961.34045
published in: Functiones et Approximatio. Commentarii Mathematici
publication date: 2000-12-14T00:00:00Z
review text: Under a suitable condition the authors prove that the solution set to the problem \(x^{(n)} = f(t,x)\), \(n\geq 2\), is a compact \(R_{\delta}\) set in the space of all continuous functions \(x:J \to E\) endowed with the metric of uniform convergence. (Here, \(f:[0,a] \times B \to E\) is a bounded continuous function, \(E\) is a Banach space and \(J= [0,h]\) where \(h \in (0,a]\) depends on \(f\) and on the radius of \(B\)).
reviewed by: Józef Myjak
Mathematics Subject Classification ID: 34G20
zbMATH DE Number: 1442081
zbMATH Keywords: differential equations
zbMATH Keywords: measure of noncompactness
zbMATH Keywords: \(R_{\delta}\) set
zbMATH Keywords: solution set
author: Stanisław Szufla
author: Aldona Szukała
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1442081