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Semiflows for Neutral Equations with State-Dependent Delays

  • Hans-Otto Walther
Chapter
Part of the Fields Institute Communications book series (FIC, volume 64)

Abstract

We show that under mild hypotheses neutral functional differential equations where delays may be state-dependent generate continuous semiflows, a larger one on a thin set in a Banach space of C1-functions and a smaller one, with better smoothness properties, on a closed subset in a Banach manifold of C2-functions. The hypotheses are satisfied for a prototype equation of the form
$$x^{\prime}(t) = a\,x^{\prime}(t + d(x(t))) + f(x(t))$$
with−h<d(x(t))<0, which for certain d and f models the interaction between following a trend and negative feedback with respect to some equilibrium state.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Mathematisches InstitutUniversitaet GiessenGiessenGermany

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