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Periodic systems

  • Jack K. Hale
  • Sjoerd M. Verduyn Lunel
Part of the Applied Mathematical Sciences book series (AMS, volume 99)

Abstract

The purpose of this chapter is to develop the theory of a linear periodic RFDE that is analogous to the Floquet theory for ordinary differential equations. It is shown by example that a complete Floquet theory does not exist. However, it is possible to define characteristic multipliers and exploit the compactness of the solution operator to show that a Floquet representation exists on the generalized eigenspace of a characteristic multiplier. The decomposition of the space C by a characteristic multiplier is also applied to the variation-of-constants formula. The case of periodic delay equations with integer lags is considered in detail.

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Copyright information

© Springer Science+Business Media New York 1993

Authors and Affiliations

  • Jack K. Hale
    • 1
  • Sjoerd M. Verduyn Lunel
    • 2
  1. 1.Georgia Institute of TechnologySchool of MathematicsAtlantaUSA
  2. 2.Vrije Universiteit AmsterdamAmsterdamThe Netherlands

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