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Periodic solutions for functional differential equations with periodic delay close to zero. (English) Zbl 1118.34056

Summary: This paper studies the existence of periodic solutions to the delay differential equation

x ˙(t)=f(x(t-μτ(t)),ε)·

The analysis is based on a perturbation method previously used for retarded differential equations with constant delay. By transforming the studied equation into a perturbed non-autonomous ordinary equation and using a bifurcation result and the PoincarĂ© procedure for this last equation, we prove the existence of a branch of periodic solutions, for the periodic delay equation, bifurcating from μ=0.

MSC:
34K13Periodic solutions of functional differential equations
34K18Bifurcation theory of functional differential equations