Geodesic
Periodic solutions for functional differential equations with periodic delay close to zero
Electronic Journal of Differential Equations, Tome 2006 (2006).

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Summary: 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 $\mu=0$.
Classification : 34K13
Keywords: differential equation, periodic delay, bifurcation, h-asymptotic stability, periodic solution 
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     author = {Hbid, My Lhassan and Qesmi, Redouane},
     title = {Periodic solutions for functional differential equations with periodic delay close to zero},
     journal = {Electronic Journal of Differential Equations},
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     volume = {2006},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a162/}
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Hbid, My Lhassan; Qesmi, Redouane. Periodic solutions for functional differential equations with periodic delay close to zero. Electronic Journal of Differential Equations, Tome 2006 (2006). http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a162/