Electron. J. Diff. Eqns., Vol. 2006(2006), No. 141, pp. 1-12.

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

My Lhassan Hbid, Redouane Qesmi

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.

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  My Lhassan Hbid
Département de Mathématiques, Faculté des Sciences Semlalia
Université Cadi Ayyad, B.P. S15, Marrakech, Morocco
email: hassan.hbid@gmail.com
Redouane Qesmi
Département de Mathématiques, Faculté des Sciences Semlalia
Université Cadi Ayyad, B.P. S15, Marrakech, Morocco
email: qesmir@gmail.com

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