abstract
We consider a scalar delay differential equation with a small parameter, and employ Walther’s method to obtain a result on the existence and stability of a slowly oscillatory periodic solution that represents a refinement of the estimate for the Lipschitz constant of a returning map. We also develop a matching method and obtain asymptotic expansions of the slowly oscillatory periodic solution and its minimal period.
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Dedicated to Professor Shui-Nee Chow on the occasion of his 60th birthday
AMS subject classifications: 34K15; 34K20; 34C25.
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Ou, C., Wu, J. Periodic Solutions of Delay Differential Equations with a Small Parameter: Existence, Stability and Asymptotic Expansion. J Dyn Diff Equat 16, 605–628 (2004). https://doi.org/10.1007/s10884-004-4294-0
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DOI: https://doi.org/10.1007/s10884-004-4294-0