Stability and attractivity of solutions of differential equations with impulses at fixed times
type: Item
instance of: scholarly article
title: Stability and attractivity of solutions of differential equations with impulses at fixed times
zbMATH Open document ID: 0995.34041
DOI: 10.1155/S1048953300000083
author: N. Delaunay
published in: Journal of Applied Mathematics and Stochastic Analysis
publication date: 2000-09-20T00:00:00Z
full work available at URL: https://eudml.org/doc/49432
review text: The authors consider two impulsive systems of the form \[ x'=F(t, x),\;t\neq t_k, \quad x(t^+_k)=x(t_k)+ I_k\bigl(x(t_k) \bigr),\;t=t_k,\quad x(t^+_0)= x_0,\tag{1} \] and \[ y'=f(t,y),\;t\neq t_k,\quad y(t^+_k)= \psi_k\bigl( y(t_k)\bigr),\;t=t_k, \quad y(t^+_0)= y_0,\tag{2} \] with solutions \(x(t)\) to (1) and \(y(t)\) to (2) and suppose that (1) and (2) are connected by a function \(v(t, x)\) which is locally Lipschitzian. Sufficient conditions for the inequality \[ v\bigl(t,x(t) \bigr)\leq \overline y(t),\;t\in\text{dom} x\cap\text{dom} \overline y, \] where \(\overline y(t)\) is an upper solution to (2) are given. Some generalized notions of well-known dynamic properties are introduced. The authors find sufficient conditions for the transfer of this properties of (2) to (1) by help of \(v(t,x)\).
reviewed by: S. Kostadinov
Mathematics Subject Classification ID: 34D30
Mathematics Subject Classification ID: 34A37
Mathematics Subject Classification ID: 34A30
Mathematics Subject Classification ID: 34D05
zbMATH DE Number: 1452805
zbMATH Keywords: impulsive differential equation
zbMATH Keywords: comparison function
zbMATH Keywords: attractivity of solutions
zbMATH Keywords: stability
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1452805