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Hopf Bifurcation for Retarded Functional Differential Equations and for Semiflows in Banach Spaces

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Abstract

We indicate how a Hopf bifurcation theorem for retarded functional differential equations can be proved correctly, following an approach that is described, but not carried out properly in the literature. Then we state and prove a Hopf bifurcation theorem for general semiflows in Banach spaces, using different methods. The general statement includes the case of retarded functional differential equations.

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Acknowledgments

Without Carla Terschlüsen’s initial contribution, namely her discovery of inaccuracies in [12, 32] and [13], the present paper would not exist. Warm thanks to her for inspiring the start of this work.

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  1. Mathematisches Institut der, Justus-Liebig-Universität Giessen, Arndtstr. 2, 35392 , Giessen, Germany

    Bernhard Lani-Wayda

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  1. Bernhard Lani-Wayda
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Correspondence to Bernhard Lani-Wayda.

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Lani-Wayda, B. Hopf Bifurcation for Retarded Functional Differential Equations and for Semiflows in Banach Spaces. J Dyn Diff Equat 25, 1159–1199 (2013). https://doi.org/10.1007/s10884-013-9334-1

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