Periodic solutions for functional differential equations with periodic delay close to zero.

*(English)*Zbl 1118.34056Summary: This paper studies the existence of periodic solutions to the delay differential equation

$$\dot{x}\left(t\right)=f(x(t-\mu \tau \left(t\right)),\epsilon )\xb7$$

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 $\mu =0$.