Open Access

Invariant foliations and stability in critical cases

Advances in Difference Equations20062006:057043

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

Received: 29 January 2006

Accepted: 3 March 2006

Published: 9 July 2006

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’ Affiliations

(1)
School of Mathematics, University of Minnesota

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Copyright

© Christian Pötzsche 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.