Variational Lyapunov Method for Difference Equations

Authors: Drici, Zahia¹; Dontha, Satyanarayana²

Source: Applicable Analysis, Volume 84, Number 4, April 2004 , pp. 363-376(14)

Publisher: Taylor and Francis Ltd

Abstract:

In this article we consider the difference equation with a smoothness condition on f with respect to y. We study the dependence of solutions of (A) on initial data and then obtain a discrete analog of Alekseev's variation of parameters formula. In addition, we develop a Variational Lyapunov Method (VLM) and use it to study the stability properties of difference equations.

Keywords: Nonlinear variation of paramaters; Variational Lyapunov method; Difference equations; Practical stability; AMS Subject Classifications: 34A07; 34D20

Document Type: Research article

DOI: http://dx.doi.org/10.1080/00036810310001632808

Affiliations: 1: Department of Mathematics and Computer Science Illinois Wesleyan University Bloomington IL 61702 USA 2: Department of Mathematical Sciences Florida Institute of Technology Melbourne FL 32901 USA

Publication date: 2004-04-01

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