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.