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Hupkes, H. J.; Verduyn Lunel, S. M.

Center manifolds for periodic functional differential equations of mixed type. (English) Zbl 1157.34052

J. Differ. Equations 245, No. 6, 1526-1565 (2008).
The behaviour of solutions of functional differential equations of mixed type near a periodic solution is investigated. More precisely, under appropriate assumptions the authors show the existence of a finite dimensional invariant manifold, which contains all solutions that stay sufficiently close to a specific periodic solution for all times. The proof of this result relies mainly on a certain discreteness condition of the Floquet spectrum, which the authors show to be satisfied for some specific model equations where the forward and backward delays are rationally related to the period of the periodic solution.
Reviewer: Marc Georgi (Berlin)

Cited in 14 Documents

MSC:

34K19 Invariant manifolds of functional-differential equations
34K17 Transformation and reduction of functional-differential equations and systems, normal forms
34K13 Periodic solutions to functional-differential equations

Keywords:

mixed type functional differential equation; Floquet theory; center manifold
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References:

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