Continuous dependence on initial values for impulsive delay differential equations.
type: Item
instance of: scholarly article
title: Continuous dependence on initial values for impulsive delay differential equations.
zbMATH Open document ID: 1085.34558
DOI: 10.1016/S0893-9659(04)90094-8
author: Xinzhi Liu
author: G. Ballinger
published in: Applied Mathematics Letters
publication date: 2005-02-25T00:00:00Z
review text: This paper studies the continuous dependence of solutions with repect to initial values for the impulsive delay differential system \[ x'(t)=f(t,x_t),\;\;t\not=\tau_k, \] \[ \Delta x(t)=I(t,x_t,\;t=\tau_k, \] with \(0=\tau_0<\tau_1<\cdots, \) and \(\lim_{k\rightarrow +\infty}\tau_k=+\infty\). Under some assumptions, the authors prove that the solutions depend continuously on the initial function.
reviewed by: Yuji Liu
Mathematics Subject Classification ID: 34K45
Mathematics Subject Classification ID: 34K05
zbMATH DE Number: 2138612
zbMATH Keywords: initial value problem
zbMATH Keywords: impulsive delay differential equation
zbMATH Keywords: continuous dependence
MaRDI profile type: Publication
cites work: Introduction to functional differential equations
cites work: Q4261600
cites work: Existence, uniqueness and boundedness results for impulsive delay differential equations
cites work: Existence and continuability of solutions for differential equations with delays and state-dependent impulses
cites work: Uniform asymptotic stability of impulsive delay differential equations
cites work: Q3995625
description: scientific article; zbMATH DE number 2138612