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Displaying similar documents to “A note on the inverse function theorem of Nash and Moser.”

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

M. Poppenberg (1999)

Studia Mathematica

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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 ( N ) , B ( R N ) , D L 1 ( N ) , for Köthe sequence spaces, and for the general class of subbinomic Fréchet algebras.