Impulsive differential systems and the pulse phenomena
type: Item
instance of: scholarly article
title: Impulsive differential systems and the pulse phenomena
zbMATH Open document ID: 0684.34003
DOI: 10.1016/0022-247X(89)90266-7
author: Shouchuan Hu
author: V. Lakshmikantham
author: S. Leela
published in: Journal of Mathematical Analysis and Applications
publication date: 1989-01-01T00:00:00Z
review text: Consider the impulsive differential system \[ (1)\quad x'=f(t,x),\quad t\neq \tau_ k(x),\quad x(t_ 0)=x_ 0,\quad t\geq 0,\quad \Delta x=I_ k(x),\quad t=\tau_ k(x), \] where \(f\in C[{\mathbb{R}}_+\times \Omega,{\mathbb{R}}^ n]\), \(\Omega \subset {\mathbb{R}}^ n\) be an open set. The solution of this system may hit a given surface, \(t=\tau_ k(x)\), finite or infinite number of times causing rhythmical beating, so called pulse phenomena. The authors give conditions such that every solution of (1) meets any given surface \(t=\tau_ k(x)\) at most once or exactly once, or several times.
reviewed by: C.Simirad
Mathematics Subject Classification ID: 34A12
zbMATH DE Number: 4120543
zbMATH Keywords: impulsive differential system
zbMATH Keywords: pulse phenomena
MaRDI profile type: Publication
cites work: Sufficient conditions for absence of ”beating” in systems of differential equations with impulses
cites work: Q4853771
description: scientific article; zbMATH DE number 4120543