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On the instability of linear nonautonomous delay systems

Raúl Naulin — 2003

Czechoslovak Mathematical Journal

The unstable properties of the linear nonautonomous delay system x ' ( 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 ' ( 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...

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