Boundedness of nonlinear differential systems with impulsive effect on random moments
type: Item
instance of: scholarly article
title: Boundedness of nonlinear differential systems with impulsive effect on random moments
zbMATH Open document ID: 1078.34512
author: Shujin Wu
author: Xianshang Meng
published in: Acta Mathematicae Applicatae Sinica. English Series
publication date: 2005-06-07T00:00:00Z
review text: Consider a system of nonlinear differential equations with impulses at random moments \[ x'(t) = f(t,x(t)) \text{ a.e.}, \quad \xi_{k-1}<t<\xi_k,\;k\in \mathbb{N}, \] \[ x(\xi_k^+)-x(\xi_k)=I_k(\tau_k,x(\xi_k)) \text{ a.e.},\quad k\in \mathbb{N}, \] \[ x(t_0)=x_0, \] where \(\xi_0=t_0\), \(\xi_k=\xi_{k-1}+\tau_k\), and \(\tau_k\) is a random variable for all \(k\in \mathbb{N}\). The authors prove some boundedness results for this system by using Lyapunov-like functions. An example is included, too.
reviewed by: Eduardo Liz
Mathematics Subject Classification ID: 34A37
Mathematics Subject Classification ID: 34D40
Mathematics Subject Classification ID: 34F05
zbMATH DE Number: 2174223
zbMATH Keywords: differential equations with impulses
zbMATH Keywords: ultimate boundedness
zbMATH Keywords: Lyapunov function
MaRDI profile type: Publication
full work available at URL: s10255-004-0157-z
OpenAlex ID: W2019202296
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DOI: 10.1007/S10255-004-0157-Z
description: scientific article; zbMATH DE number 2174223