Global stability for nonlinear dynamic equations with variable coefficients
type: Item
instance of: scholarly article
title: Global stability for nonlinear dynamic equations with variable coefficients
zbMATH Open document ID: 1152.34033
author: Douglas R. Anderson
published in: Journal of Mathematical Analysis and Applications
publication date: 2008-07-10T00:00:00Z
review text: The author considers nonlinear dynamic equations on a time scale \(\mathbb{T}\) which can be any non-empty closed subset of the real numbers that is unbounded above. This unified approach encompasses dynamical systems governed by differential equations, difference equations and combinations of both. Additionally, time delays are allowed. The considered equations are of the form \[ x^\Delta(t) = -\sum_{j=0}^n a_j(t) f_j(x(\tau_j(t)), \] where \(x^\Delta\) is the so-called delta derivative, \(\tau_1,\tau_2,\ldots,\tau_n\) are time varying time delays, \(a_1,a_2,\ldots,a_n\) are non-negative time varying coefficients, and \(f_1,f_2,\ldots,f_n\) are continuous functions such that \(f_j(0)=0\), \(f_j(x)\geq 0\) and \(f_j(-x)\geq 0\) for all \(j=0,1,\ldots,n\) and all \(x\geq 0\). Sufficient conditions are given for which the zero solution is globally asymptotically stable. The results are illustrated with two examples.
reviewed by: Stephan Trenn
Mathematics Subject Classification ID: 34D23
Mathematics Subject Classification ID: 39A10
zbMATH DE Number: 5299484
zbMATH Keywords: dynamic equations
zbMATH Keywords: times scales
zbMATH Keywords: stability
MaRDI profile type: Publication
full work available at URL: j.jmaa.2008.05.001
OpenAlex ID: W2060683436
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DOI: 10.1016/J.JMAA.2008.05.001
description: scientific article; zbMATH DE number 5299484