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Smooth centre manifolds for impulsive delay differential equations

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existence-smoothness3.pdf (556.54 KB)

Date

2018-04-16

Authors

Church, Kevin E. M.
Liu, Xinzhi

Journal Title

Journal ISSN

Volume Title

Publisher

Elsevier

Abstract

The existence and smoothness of centre manifolds and a reduction principle are proven for impulsive delay differential equations. Several intermediate results of theoretical interest are developed, including a variation of constants formula for linear equations in the phase space of right-continuous regulated functions, linear variational equation and smoothness of the nonautonomous process, and a Floquet theorem for periodic systems. Three examples are provided to illustrate the results.

Description

Preprint of an article published in Journal of Differential Equations, available at: https://doi.org/10.1016/j.jde.2018.04.021

Keywords

Centre manifold, Impulsive delay differential equation, Lyapunov–Perron method, Variation-of-constants formula, Floquet theorem

LC Keywords

Citation

URI

https://doi.org/10.1016/j.jde.2018.04.021
 http://hdl.handle.net/10012/13105

Collections

Waterloo Research
Applied Mathematics