On the instability of differential systems with varying delay
type: Item
instance of: scholarly article
title: On the instability of differential systems with varying delay
zbMATH Open document ID: 1020.34065
DOI: 10.1016/S0022-247X(02)00301-3
published in: Journal of Mathematical Analysis and Applications
publication date: 2003-02-11T00:00:00Z
review text: The paper is devoted to delay differential systems of the form \[ \dot{x}(t)=A(t)x(t)+B(t)x(t-r_1(t))+f(t,x(t),x(t-r_2(t))), \quad t\geq 0, \tag{1} \] where \(x=(x_1,\ldots,x_n)\), \(f(t,0,0)=0\), the delays \(r_1\) and \(r_2\) are continuous and bounded and \(A(t)\) and \(B(t)\) are continuous matrices. The author extends Coppel's instability theorem [\textit{W. A. Coppel}, J. Lond. Math. Soc. 39, 255-260 (1964; Zbl 0128.08205)] to delay differential systems (1). Several simple illustrative examples are given.
Mathematics Subject Classification ID: 34K20
zbMATH DE Number: 1866629
zbMATH Keywords: Lyapunov instability
zbMATH Keywords: delay differential systems
author: Raúl Naulin
reviewed by: Oleg Anashkin
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1866629