Difference equations of Volterra type and extension of Lyapunov's method
type: Item
instance of: scholarly article
title: Difference equations of Volterra type and extension of Lyapunov's method
zbMATH Open document ID: 0732.39004
DOI: 10.1155/S1048953390000181
author: M. Zouyousefain
published in: Journal of Applied Mathematics and Stochastic Analysis
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/46614
review text: The author studies the nonlinear difference equation of Volterra type (1) \(\Delta x(n)=f(n,x(n),\sum^{n-1}_{s=n_ 0}G(n,s,x(s))),\) \(x(n_ 0)=n_ 0, n_ 0\in {\mathbb{N}}^+_{n_ 0},\) where \(f,G:{\mathbb{N}}^+_{n_ 0}\times {\mathbb{R}}^ d\times {\mathbb{R}}^ d\to {\mathbb{R}}^ d.\) With the help of an extension of Lyapunov's method and choosing a minimal class of suitable functions the author obtains conditions for the stability properties of (1). Another approach used by author is an estimation of the variation of Lyapunov's function by means of some functional.
Mathematics Subject Classification ID: 39A10
Mathematics Subject Classification ID: 39A11
zbMATH DE Number: 4210732
zbMATH Keywords: asymptotic stability
zbMATH Keywords: comparison methods
zbMATH Keywords: linearization method
zbMATH Keywords: nonlinear difference equation of Volterra type
zbMATH Keywords: Lyapunov's method
reviewed by: Yu. V. Kostarchuk
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4210732