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Center manifolds for delay-differential equations with variable argument

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Abstract

For delay-differential equations with piecewise constant delay, we construct center invariant manifolds with the optimal regularity. More precisely, we consider perturbations that are either globally Lipschitz or of class \(C^1\). More generally, we consider Lipschitz and \(C^1\) perturbations of evolution families that need not be invertible and need not have bounded growth. Nevertheless, the solutions in the center invariant manifold are always unique and global.

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Authors and Affiliations

  1. Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, 1049-001, Lisboa, Portugal

    Luis Barreira & Claudia Valls

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  1. Luis Barreira
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  2. Claudia Valls
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Correspondence to Luis Barreira.

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Supported by FCT/Portugal through CAMGSD, IST-ID, projects UIDB/04459/2020 and UIDP/04459/2020.

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Barreira, L., Valls, C. Center manifolds for delay-differential equations with variable argument. Period Math Hung 86, 172–190 (2023). https://doi.org/10.1007/s10998-022-00469-3

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