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Topics in Delay Differential Equations

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Abstract

We introduce delay differential equations, give some motivation by applications, review basic facts about initial value problems from wellposedness to the variation-of-constants formula in the sun-star-framework, and discuss two topics in greater detail: (a) The dynamics generated by autonomous scalar equations with a single, constant time lag, from existence of periodic solutions to the fine structure of global attractors and chaotic motion, and (b) more recent results on equations with state-dependent delay (lack of smoothness, differentiable solution operators on suitable Banach manifolds, case studies). The final part addresses directions of future research.

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    Hans-Otto Walther

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Walther, HO. Topics in Delay Differential Equations. Jahresber. Dtsch. Math. Ver. 116, 87–114 (2014). https://doi.org/10.1365/s13291-014-0086-6

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