Smooth centre manifolds for impulsive delay differential equations

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.