Linearization near the integral manifold for a system of differential equations with piecewise constant argument
type: Item
instance of: scholarly article
title: Linearization near the integral manifold for a system of differential equations with piecewise constant argument
zbMATH Open document ID: 0892.34045
author: G. Papaschinopoulos
published in: Journal of Mathematical Analysis and Applications
publication date: 1998-04-29T00:00:00Z
review text: Assuming exponential dichotomy conditions with respect to the continuous matrix function \( A \), the existence of a homeomorphism sending the solutions of the differential equation with piecewise constant arguments \[ x'(t)=B(t)x([t])+f(t,x(t),y(t)), \quad y'(t)=A(t)y(t)+C(t)y([t])+g(t,x(t),y(t))\tag{1} \] into solutions of the reduced equation \[ x'(t)=B(t)x([t])+f(t,x(t),v(t,x(t))), \qquad y'(t)=A(t)y(t)\tag{2} \] is proved. Here \(y=v(t,x)\) describes an integral manifold of (1) whose existence is shown in a former paper. It is assumed that the continuous matrix functions \( B \) and \(C \) are sufficiently small and that the continuous nonlinearities \(f \) and \(g \) are small Lipschitzian. The admissible bounds for \( B \), \(C \) and the admissible Lipschitz constants for \( f \) and \( g\) are expressed in terms of the bound for \( A \) and its dichotomy properties.
Mathematics Subject Classification ID: 34C45
Mathematics Subject Classification ID: 34C30
Mathematics Subject Classification ID: 34C20
zbMATH DE Number: 1115418
zbMATH Keywords: linearization
zbMATH Keywords: piecewise constant arguments
zbMATH Keywords: integral manifolds
zbMATH Keywords: reduction
zbMATH Keywords: exponential dichotomy
reviewed by: Norbert Koksch
MaRDI profile type: Publication
full work available at URL: jmaa.1997.5579
OpenAlex ID: W2065146536
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DOI: 10.1006/JMAA.1997.5579
description: scientific article; zbMATH DE number 1115418