A Floquet-Liapunov theorem in Fréchet spaces

• George N. Galanis ^[1] ; Efstathios E. Vassiliou ^[1]
  1. [1] University of Athens, Greece
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 27, Nº 3-4, 1998, págs. 427-436
• Idioma: inglés
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• Resumen

  • Based on [4], we prove a variation of the theorem in title, for equations with periodic coefficients, in Frechet spaces. The main result gives equivalent conditions ensuring the reduction of such an equation to one with constant coefficient.

    In the particular case of Coo, we obtain the exact analogue of the classical theorem. Our approach essentially uses the fact that a Frechet space is the limit of a projective sequence of Banach spaces. This method can also be applied for a geometric interpretation of the same theorem within the context of total differential equations in Frechet fiber bundles.