Well-posedness of the Cauchy problem for nonlinear differential equations with variable delays
type: Item
instance of: scholarly article
title: Well-posedness of the Cauchy problem for nonlinear differential equations with variable delays
zbMATH Open document ID: 1094.34045
DOI: 10.1023/B:DIEQ.0000035774.29859.22
author: Guram L. Kharatishvili
author: T. Tadumadze
published in: Differential Equations
publication date: 2005-06-17T00:00:00Z
review text: The authors consider the nonlinear delay differential equation \[ x'(t)=f(t,x(\tau_1(t)),\dots,x(\tau_j(t))), \] where \(x\in\mathbb R^n\), \(\tau_i(t)\leq t\), \(\tau_i'(t)> 0\), \(i =1,\dots,s\), and \(f\) satisfies certain boundedness and Lipschitz conditions. Under certain assumptions, the author proves that the solution depends continuously on the initial data and on small perturbations of the function \(f\).
Mathematics Subject Classification ID: 34K05
Mathematics Subject Classification ID: 34A12
zbMATH DE Number: 2176620
zbMATH Keywords: delay differential equations
zbMATH Keywords: Cauchy problems
zbMATH Keywords: nonlinear equations
reviewed by: Stig-Olof Londen
MaRDI profile type: Publication
full work available at URL: b:dieq.0000035774.29859.22
OpenAlex ID: W2043766503
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description: scientific article; zbMATH DE number 2176620