Retarded differential equations with piecewise constant delays
type: Item
instance of: scholarly article
title: Retarded differential equations with piecewise constant delays
zbMATH Open document ID: 0557.34059
DOI: 10.1016/0022-247X(84)90248-8
author: Joseph Wiener
author: Kenneth Cooke
published in: Journal of Mathematical Analysis and Applications
publication date: 1984-01-01T00:00:00Z
review text: Functional differential equations with piecewise constant delays are studied. They are closely related to impulse, loaded and, especially, to difference equations, and have the structure of continuous dynamical systems within intervals of unit length. Continuity of a solution at a point joining any two consecutive intervals implies recursion relations for the solution at such points. The equations are thus similar in structure to those found in certain ''sequential-continuous'' models of disease dynamics. The main feature of equations with piecewise constant delays is that it is natural to pose initial-value and boundary-value problems for them not on intervals but at a certain number of individual points. Existence and uniqueness theorems are established for equations with bounded and unbounded operators. A general estimate of the solutions' growth as \(t\to +\infty\) is found. Special consideration is given to the problem of stability, and oscillatory properties of solutions are studied, too. The instrument of continued fractions plays an important role in the computation of solutions and in the analysis of their asymptotic behavior. Equations with unbounded delay arise in cases of several argument deviations. In such problems, the initial function is prescribed on (-\(\infty,0]\) and the solution is sought for \(t>0\).
Mathematics Subject Classification ID: 34K05
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 34K30
Mathematics Subject Classification ID: 39A10
zbMATH DE Number: 3888112
zbMATH Keywords: greatest-integer function
zbMATH Keywords: Functional differential equations
zbMATH Keywords: piecewise constant delays
zbMATH Keywords: difference equations
zbMATH Keywords: continuous dynamical systems
zbMATH Keywords: growth
MaRDI profile type: Publication
cites work: Q5565859
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full work available at URL: 0022-247x(84)90248-8
OpenAlex ID: W2008117223
description: scientific article; zbMATH DE number 3888112