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On the instability of linear nonautonomous delay systems. (English) Zbl 1080.34543
Summary: 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 delay function.

##### MSC:
 34D20 Stability of solutions to ordinary differential equations 34D05 Asymptotic properties of solutions to ordinary differential equations
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##### References:
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