On the linearization theorem for nonautonomous differential equations
type: Item
instance of: scholarly article
title: On the linearization theorem for nonautonomous differential equations
zbMATH Open document ID: 1331.34065
author: N. E. Zubov
published in: Bulletin des Sciences Mathématiques
publication date: 2015-10-30T00:00:00Z
review text: In [J. Math. Anal. Appl. 41, 753--758 (1973; Zbl 0272.34056)], \textit{K. J. Palmer} proposed some generalization of the Hartman and Grobman's linearization theorem [\textit{P. Hartman}, Ordinary differential equations. York-London-Sydney: John Wiley and Sons, Inc (1964; Zbl 0125.32102)] to the nonautonomous case. Here, the authors consider the system \[ x_1'=A_1(t)x_1+f(t,x),\;\; x_2'=A_2(t)x_2,\;\;x=(x_1,x_2)\in \mathbb R^{n+m} \] and extend Palmer's result in two directions: (1) the nonlinear term might be unbounded or not Lipschitz continuous, and (2) only \(x_1'=A_1(t)x_1\) possesses an exponential dichotomy.
Mathematics Subject Classification ID: 34C20
Mathematics Subject Classification ID: 34D30
Mathematics Subject Classification ID: 34D09
Mathematics Subject Classification ID: 37C60
zbMATH DE Number: 6502605
zbMATH Keywords: as stated
reviewed by: Iliya D. Iliev
MaRDI profile type: Publication
full work available at URL: j.bulsci.2014.12.005
OpenAlex ID: W2054935363
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DOI: 10.1016/J.BULSCI.2014.12.005
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description: scientific article; zbMATH DE number 6502605