PERIODIC SOLUTIONS FOR FUNCTIONAL DIFFERENTIAL EQUATIONS WITH PERIODIC DELAY CLOSE TO ZERO

This paper studies the existence of periodic solutions to the delay differential equation x(overdot) (t) = f(x(t - mu(t)), is an element of). 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 Poincare procedure for this last equation, we prove the existence of a branch of periodic solutions, for the periodic delay equation, bifurcating from mu = 0.