Time transformations for delay differentialequations

Hermann Brunner; Stefano Maset

doi:10.3934/dcds.2009.25.751

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2009, Volume 25, Issue 3: 751-775. Doi: 10.3934/dcds.2009.25.751

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Time transformations for delay differential equations

Hermann Brunner^1, and
Stefano Maset^2,

1.
Department of Mathematics, Hong Kong Baptist University, Hong Kong
2.
Dipartimento di Matematica e Informatica, Università di Trieste, I-34100 Trieste

Received: May 31, 2008

Revised: February 28, 2009

Published: August 2009

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Abstract

We study changes of variable, called time transformations, which reduce a delay differential equation (DDE) with a variable non-vanishing delay and an unbounded lag function to another DDE with a constant delay. By using this reduction, we can easily obtain a superconvergent integration of the original equation, even in the case of a non-strictly-increasing lag function, and study the type of decay to zero of solutions of scalar linear non-autonomous equations with a strictly increasing lag function.

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Mathematics Subject Classification: 34K17, 34K28, 34K20.

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