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September  2009, 25(3): 751-775. doi: 10.3934/dcds.2009.25.751

Time transformations for delay differential equations

Hermann Brunner 1, and  Stefano Maset 2,

1. 

Department of Mathematics, Hong Kong Baptist University, Hong Kong, China
2. 

Dipartimento di Matematica e Informatica, Università di Trieste, I-34100 Trieste, Italy

Received  June 2008 Revised  March 2009 Published  August 2009

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.
Keywords: Delay differential equations, changes of variable, superconvergence, variable delays, asymptotic stability..
Mathematics Subject Classification: 34K17, 34K28, 34K2.
Citation: Hermann Brunner, Stefano Maset. Time transformations for delay differential equations. Discrete and Continuous Dynamical Systems, 2009, 25 (3) : 751-775. doi: 10.3934/dcds.2009.25.751
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