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Linearized Stability for Semiflows Generated by a Class of Neutral Equations, with Applications to State-Dependent Delays

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Abstract

We prove a principle of linearized stability for semiflows generated by neutral functional differential equations of the form x′(t) = g(∂ x t , x t ). The state space is a closed subset in a manifold of C 2-functions. Applications include equations with state-dependent delay, as for example x′(t) = a x′(t + d(x(t))) + f (x(t + r(x(t)))) with \({a\in\mathbb{R}, d:\mathbb{R}\to(-h,0), f:\mathbb{R}\to\mathbb{R}, r:\mathbb{R}\to[-h,0]}\).

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  1. Mathematisches Institut, Universität Giessen, Arndtstr. 2, 35392, Giessen, Germany

    Hans-Otto Walther

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  1. Hans-Otto Walther
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Correspondence to Hans-Otto Walther.

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This paper is dedicated to Professor Jack Hale on the occasion of his 80th birthday.

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Walther, HO. Linearized Stability for Semiflows Generated by a Class of Neutral Equations, with Applications to State-Dependent Delays. J Dyn Diff Equat 22, 439–462 (2010). https://doi.org/10.1007/s10884-010-9168-z

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  • DOI: https://doi.org/10.1007/s10884-010-9168-z

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