A generalization of the monodromy operator for non-periodic linear differential equations
type: Item
instance of: scholarly article
title: A generalization of the monodromy operator for non-periodic linear differential equations
zbMATH Open document ID: 0881.34086
author: Nguyen Van Minh
author: Bernd Aulbach
author: Peter P. Zabreĭko
published in: Differential Equations and Dynamical Systems
publication date: 1998-01-22T00:00:00Z
review text: Let \({dx\over dt}=A(t)x\) be a system of ordinary differential equations in a complex Banach space \(X\), where the real variable \(t\) belongs to an interval \([a,\infty)\) for some fixed \(a\in\mathbb{R}\cup-\infty\). In the paper the notion of a characteristic operator for such systems is introduced. The authors establish the formula relating the spectrum of the characteristic operator to the general exponent of the equations and describe conditions for stability or exponential dichotomy in terms of this operator. It is shown that the characteristic operator generalizes the monodromy operator for periodic equations. The perturbation results which extend previous ones from \textit{W. A. Coppel} [Lect. Notes Math. 629 (1978; Zbl 0376.34001)] and \textit{Yu. L. Daleckii} and \textit{M. G. Krein} [Am. Math. Soc. VI, (1974; Zbl 0286.34094)] is obtained.
Mathematics Subject Classification ID: 34L05
Mathematics Subject Classification ID: 34C99
Mathematics Subject Classification ID: 34D99
zbMATH DE Number: 1010997
zbMATH Keywords: characteristic operator
zbMATH Keywords: stability or exponential dichotomy
zbMATH Keywords: monodromy operator
reviewed by: Mykola Grygorenko
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1010997