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  • Research Article
  • 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:

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.

Keywords

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

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Authors’ Affiliations

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

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