Justification of partially-multiplicative averaging for a class of functional-differential equations with variable structure and impulses
type: Item
instance of: scholarly article
title: Justification of partially-multiplicative averaging for a class of functional-differential equations with variable structure and impulses
zbMATH Open document ID: 0578.34048
author: S. D. Milusheva
author: Drumi Bainov
published in: Tsukuba Journal of Mathematics
publication date: 1985-01-01T00:00:00Z
review text: The averaging method is justified for the first time for a class of functional-differential equations of neutral type with variable structure and impulses. The system under consideration is of the form \(\dot x(t)=\mu A(t,x_ t,\dot x_ t) X(t,x(t)),\) \(t\neq t_ i(x)\), where \(x_ t=x(h(t,x(t)))\) and \(\mu >0\) is a small parameter. For \(t=t_ i(x)\) the trajectory is subject to instant jumps (of order \(\mu)\) and the matrix A(.) is also changed. The averaged system however is of constant structure and without impulses. This clearly simplifies the qualitative investigation and the integration of this class of functional- differential equations.
Mathematics Subject Classification ID: 34K99
Mathematics Subject Classification ID: 34C29
zbMATH DE Number: 3925340
zbMATH Keywords: averaging method
zbMATH Keywords: neutral type
zbMATH Keywords: functional-differential equations
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.21099/tkbjm/1496160190
OpenAlex ID: W388181129
DOI: 10.21099/TKBJM/1496160190
description: scientific article; zbMATH DE number 3925340