Anti-Lyapunov method for systems of discrete equations
type: Item
instance of: scholarly article
title: Anti-Lyapunov method for systems of discrete equations
zbMATH Open document ID: 1065.39008
author: Josef Diblík
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2004-10-04T00:00:00Z
review text: Sufficient conditions for the boundedness of solutions of the discrete system \[ U_{i}(k+1) = U_{i}(k) + F_{i}(k, \underline{U}(k) \tag{1} \] are considered. By imposing the conditions of Lipschitz, convexity, retract and strict regress-type property the author proves that there exists a solution which belongs to a given open bounded and connected set. Then he gives a variant of the above result using the concept of a polyfacial regular set. He applies his results to the nonlinear system \[ U_{i}(k+1) = \mu_{i}(k)U_{i}(k) + W_{i} (k,\underline{U}(k)) \tag{2} \] and obtains sufficient conditions that the solution \(\underline{U}(k)\) is \(\delta \)-bounded i.e. \( \| \underline{U} \| < \delta \). An example is given. Finally some open problems are discussed.
Mathematics Subject Classification ID: 39A11
Mathematics Subject Classification ID: 39A10
zbMATH DE Number: 2106070
zbMATH Keywords: asymptotic behaviour
zbMATH Keywords: bounded solution
zbMATH Keywords: retraction
zbMATH Keywords: nonlinear system
reviewed by: Ahmed Hegazi
MaRDI profile type: Publication
full work available at URL: j.na.2004.03.030
OpenAlex ID: W2032344729
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DOI: 10.1016/J.NA.2004.03.030
description: scientific article; zbMATH DE number 2106070