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Invariant foliations and stability in critical cases

Advances in Difference Equations volume 2006, Article number: 057043 (2006) Cite this article

Abstract

We construct invariant foliations of the extended state space for nonautonomous semilinear dynamic equations on measure chains (time scales). These equations allow a specific parameter dependence which is the key to obtain perturbation results necessary for applications to an analytical discretization theory of ODEs. Using these invariant foliations we deduce a version of the Pliss reduction principle.

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Authors and Affiliations

  1. School of Mathematics, University of Minnesota, 206 Church Street SE, Minneapolis, MN, 55455, USA

    Christian Pötzsche

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  1. Christian Pötzsche
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Correspondence to Christian Pötzsche.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Pötzsche, C. Invariant foliations and stability in critical cases. Adv Differ Equ 2006, 057043 (2006). https://doi.org/10.1155/ADE/2006/57043

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  • DOI: https://doi.org/10.1155/ADE/2006/57043

Keywords

  • Differential Equation
  • Partial Differential Equation
  • State Space
  • Ordinary Differential Equation
  • Functional Analysis