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

• Autorzy: M. Poppenberg
• Języki publikacji: EN

Abstrakty

EN

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 $C^∞(K)$, $S(ℝ^N)$, $B(ℝ R^N)$, $D_{L_1}(ℝ^N)$, for Köthe sequence spaces, and for the general class of subbinomic Fréchet algebras.

Kategorie tematyczne

• 46A04: Locally convex Fr\'echet spaces and (DF)-spaces
• 46A45: Sequence spaces (including K\"othe sequence spaces)
• 34G10: Linear equations
• 58C15: Implicit function theorems; global Newton methods
• 34A12: Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions
• 34G20: Nonlinear equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1999
• Tom: 137
• Numer: 2
• Strony: 101-121

Daty

wydano

1999

otrzymano

1996-11-29

poprawiono

1999-05-05

Twórcy

autor

M. Poppenberg

• Fachbereich Mathematik, Universität Dortmund, D-44221 Dortmund, Germany

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