Continuity in functional differential equations with infinite delay
type: Item
instance of: scholarly article
title: Continuity in functional differential equations with infinite delay
zbMATH Open document ID: 0743.34068
DOI: 10.1007/BF02005972
author: Youhe Feng
author: T. A. Burton
published in: Acta Mathematicae Applicatae Sinica. English Series
publication date: 1992-06-27T00:00:00Z
review text: A continuity approach is presented for the equation (1) \(\dot x=f(t,x_ t)\) with infinite delay, where the function \(f\) satisfies a so-called fading memory condition. The space \(X\) of the initial functions is endowed with two topologies (the sup-norm topology and a \(g\)-norm topology). The authors investigate when (i) continuity of the solution \(x(t,0,\varphi)\) in \(\varphi\) (with respect to the \(g\)-topology) is equivalent to uniqueness, and (ii) \(x(t,0,\varphi)\) is jointly continuous in \((t,\varphi)\). An application is given for the Poincaré mapping generated from the solutions of equation (1).
Mathematics Subject Classification ID: 34K05
zbMATH DE Number: 25922
zbMATH Keywords: functional differential equations
zbMATH Keywords: continuous dependence
zbMATH Keywords: fading memory
reviewed by: George Karakostas
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 25922