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Title

An application of the Nash-Moser theorem to ordinary differential equations in Fréchet spaces

Authors 1

Affiliations

  1. Fachbereich Mathematik, Universität Dortmund, D-44221 Dortmund, Germany

Abstract

A general existence and uniqueness result of Picard-Lindelöf type is proved for ordinary differential equations in Fréchet spaces as an application of a generalized Nash-Moser implicit function theorem. Many examples show that the assumptions of the main result are natural. Applications are given for the Fréchet spaces C∞(K), S(ℝN), B(ℝRN), DL1(ℝN), for Köthe sequence spaces, and for the general class of subbinomic Fréchet algebras.

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Studia Mathematica
1999/137/2
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Pages:
101-121
Main language of publication
English
Received
1996-11-29
Accepted
1999-05-05
Published
1999
Exact and natural sciences