Stability of continuous and discrete Volterra integro-differential equations by Liapunov approach
type: Item
instance of: scholarly article
title: Stability of continuous and discrete Volterra integro-differential equations by Liapunov approach
zbMATH Open document ID: 0858.45008
published in: Journal of Integral Equations and Applications
publication date: 1996-08-21T00:00:00Z
review text: The authors extend results from the classical Lyapunov stability theory for ordinary differential equations to systems of Volterra integro-differential equations. (No reference is made to related results obtained in recent years by, for example, \textit{T. A. Burton}: Stability and periodic solutions of ordinary and functional differential equations, Academic Press, Orlando, (1985; Zbl 0635.34001).) An analogous theory is then developed for difference equations of unbounded order, and the results are illustrated by applying them to difference equations arising in the discretization of Volterra integro-differential equations by linear multistep methods. There are no examples, and it appears that (at present) this discrete theory has limited application in concrete situations.
Mathematics Subject Classification ID: 45M10
Mathematics Subject Classification ID: 39A10
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45J05
Mathematics Subject Classification ID: 45G15
zbMATH DE Number: 885489
zbMATH Keywords: discrete Volterra integro-differential equations
zbMATH Keywords: Lyapunov method
zbMATH Keywords: Lyapunov stability
zbMATH Keywords: systems of Volterra integro-differential equations
zbMATH Keywords: difference equations
zbMATH Keywords: linear multistep methods
author: M. R. Crisci
author: V. B. Kolmanovskii
author: Elvira Russo
author: Antonia Vecchio
reviewed by: H. Brunner
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/jiea/1181075895
OpenAlex ID: W2032116788
cites work: Q3750978
cites work: Q4229393
cites work: Q4002473
cites work: Note on a Nonlinear Volterra Equation
cites work: Q3681889
DOI: 10.1216/JIEA/1181075895
description: scientific article; zbMATH DE number 885489