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Zbl 1118.34056
Hbid, My Lhassan; Qesmi, Redouane
Periodic solutions for functional differential equations with periodic delay close to zero. (English)
[J] Electron. J. Differ. Equ. 2006, Paper No. 141, 12 p., electronic only (2006). ISSN 1072-6691/e

Summary: This paper studies the existence of periodic solutions to the delay differential equation $$\dot{x}(t)=f(x(t-\mu\tau(t)),\varepsilon).$$ 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 Poincaré procedure for this last equation, we prove the existence of a branch of periodic solutions, for the periodic delay equation, bifurcating from $\mu=0$.

MSC 2000:: *34K13 Periodic solutions of functional differential equations
34K18 Bifurcation theory of functional differential equations

Keywords: bifurcation; $h$-asymptotic stability

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