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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
\[ \dot{x}(t)=f(x(t-\mu\tau(t)),\varepsilon). \]
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 Poincaré procedure for this last equation, we prove the existence of a branch of periodic solutions, for the periodic delay equation, bifurcating from \(\mu=0\).

MSC:

34K13 Periodic solutions to functional-differential equations
34K18 Bifurcation theory of functional-differential equations
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