On the asymptotic stability of the solutions of functional differential equations with infinite delay
type: Item
instance of: scholarly article
title: On the asymptotic stability of the solutions of functional differential equations with infinite delay
zbMATH Open document ID: 0797.34078
author: Géza Makay
published in: Journal of Differential Equations
publication date: 1994-10-13T00:00:00Z
review text: Let \(W: R_ +\to R_ +\) be continuous, strictly increasing with \(W(0)= 0\), and let \(g: R_ -\to R_ +\) be integrable. The author gives sufficient conditions for uniform asymptotic stability of the zero solution using a Lyapunov functional \(V\) whose derivative is negative definite along any solution \(x\) in one of the following two senses: \[ V'(t,x_ t)\leq -\eta(t)W\left(\int^ 0_{-\infty} | x(t+s)| g(s)ds\right),\tag{1} \] \[ V'(t,x_ t)\leq -\eta(t)W(| x(t)|),\tag{2} \] where \(\eta\) is a suitable nonnegative scalar function.
Mathematics Subject Classification ID: 34K20
zbMATH DE Number: 554306
zbMATH Keywords: uniform asymptotic stability
zbMATH Keywords: Lyapunov functional
reviewed by: László Hatvani
MaRDI profile type: Publication
OpenAlex ID: W2080745372
DOI: 10.1006/JDEQ.1994.1029
description: scientific article; zbMATH DE number 554306