Displaying similar documents to “On approximation of the solutions of delay differential equations by using piecewise constant arguments.”

On the instability of linear nonautonomous delay systems

Raúl Naulin (2003)

Czechoslovak Mathematical Journal

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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...