Justification of the averaging method for a system of functional- differential equations with variable structure and impulses
type: Item
instance of: scholarly article
title: Justification of the averaging method for a system of functional- differential equations with variable structure and impulses
zbMATH Open document ID: 0648.34079
DOI: 10.1007/BF01442183
author: S. D. Milusheva
author: Drumi Bainov
published in: Applied Mathematics and Optimization
publication date: 1987-01-01T00:00:00Z
review text: The method of averaging is justified for a system of functional differential equations with variable structure (the right-hand side of the equation changes when the solution \(x: T\to {\mathbb{R}}^ n\) meets a given hypersurface \(f(t,x)=0\) in the extended state space \(T\times {\mathbb{R}}^ n)\), impulses (the solution ``jumps'' when meeting a hypersurface of the type \(t=t_ i(x))\) and a deviating argument depending on both x and t. The averaging scheme strongly simplifies the problem since it leads to an usual Cauchy problem for an ordinary differential equation in \({\mathbb{R}}^ n\).
Mathematics Subject Classification ID: 34K99
Mathematics Subject Classification ID: 34C29
zbMATH DE Number: 4058010
zbMATH Keywords: method of averaging
zbMATH Keywords: functional differential equations with variable structure
zbMATH Keywords: impulses
zbMATH Keywords: Cauchy problem
reviewed by: Mihail M. Konstantinov
MaRDI profile type: Publication
cites work: Justification of the averaging method for a system of differential equations with fast and slow variables and with impulses
cites work: Q5560446
cites work: Q5341131
description: scientific article; zbMATH DE number 4058010