Smooth centre manifolds for impulsive delay differential equations
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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.
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Kevin E.M. Church, Xinzhi Liu (2018). Smooth centre manifolds for impulsive delay differential equations. UWSpace. http://hdl.handle.net/10012/13105