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Title: On the instability of linear nonautonomous delay systems (English)
Author: Naulin, Raúl
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 53
Issue: 3
Year: 2003
Pages: 497-514
Summary lang: English
Category: math
Summary: The unstable properties of the linear nonautonomous delay system $x^{\prime }(t)=A(t)x(t)+B(t)x(t-r(t))$, with nonconstant delay $r(t)$, are studied. It is assumed that the linear system $y^{\prime }(t)=(A(t)+B(t))y(t)$ is unstable, the instability being characterized by a nonstable manifold defined from a dichotomy to this linear system. The delay $r(t)$ is assumed to be continuous and bounded. Two kinds of results are given, those concerning conditions that do not include the properties of the delay function $r(t)$ and the results depending on the asymptotic properties of the delay function. (English)
Keyword: Liapounov instability
Keyword: $h$-instability
Keyword: instability of delay equations
Keyword: nonconstant delays
MSC: 34D05
MSC: 34D09
MSC: 34D20
MSC: 34K06
MSC: 34K20
idZBL: Zbl 1080.34543
idMR: MR2000048
Date available: 2009-09-24T11:03:48Z
Last updated: 2020-07-03
Stable URL:
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