Electronic Journal of Differential Equations,
Vol. 2006(2006), No. 141, pp. 1-12.

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

Authors: My Lhassan Hbid (Univ. Cadi Ayyad, Marrakech, Morocco)
         Redouane Qesmi  (Univ. Cadi Ayyad, Marrakech, Morocco)
	 
Abstract: 
 This paper studies the existence of periodic solutions to the
 delay differential equation
 $$
 \dot{x}(t)=f(x(t-\mu\tau(t)),\epsilon)\,.
 $$
 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 $\mu=0$.
 
Submitted August 25, 2006. Published November 9, 2006.
Math Subject Classifications: 34K13.
Key Words: Differential equation; periodic delay; 
     bifurcation; h-asymptotic stability; periodic solution.