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arXiv · 1910.04808

Expansions in the delay of quasi-periodic solutions for state dependent delay equations

Alfonso Casal·Livia Corsi·Rafael de la Llave
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Abstract

We consider several models of State Dependent Delay Differential Equations (SDDEs), in which the delay is affected by a small parameter. This is a very singular perturbation since the nature of the equation changes. Under some conditions, we construct formal power series, which solve the SDDEs order by order. These series are quasi-periodic functions of time. This is very similar to the Lindstedt procedure in celestial mechanics. Truncations of these power series can be taken as input for a-posteriori theorems, that show that near the approximate solutions there are true solutions. In this way, we hope that one can construct a catalogue of solutions for SDDEs, bypassing the need of a systematic theory of existence and uniqueness for all initial conditions.

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Alfonso Casal, Livia Corsi, Rafael de la Llave. 2019-10-10. Expansions in the delay of quasi-periodic solutions for state dependent delay equations. https://doi.org/10.1088/1751-8121/ab7b9e

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