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

M. Poppenberg

Studia Mathematica (1999)

  • Volume: 137, Issue: 2, page 101-121
  • ISSN: 0039-3223

Abstract

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

How to cite

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Poppenberg, M.. "An application of the Nash-Moser theorem to ordinary differential equations in Fréchet spaces." Studia Mathematica 137.2 (1999): 101-121. <http://eudml.org/doc/216678>.

@article{Poppenberg1999,
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 $C^∞(K)$, $S(ℝ^N)$, $B(ℝ R^N)$, $D_\{L_1\}(ℝ^N)$, for Köthe sequence spaces, and for the general class of subbinomic Fréchet algebras.},
author = {Poppenberg, M.},
journal = {Studia Mathematica},
keywords = {existence; uniqueness; Nash-Moser implicit function theorem; subbinomic Fréchet algebras},
language = {eng},
number = {2},
pages = {101-121},
title = {An application of the Nash-Moser theorem to ordinary differential equations in Fréchet spaces},
url = {http://eudml.org/doc/216678},
volume = {137},
year = {1999},
}

TY - JOUR
AU - Poppenberg, M.
TI - An application of the Nash-Moser theorem to ordinary differential equations in Fréchet spaces
JO - Studia Mathematica
PY - 1999
VL - 137
IS - 2
SP - 101
EP - 121
AB - 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.
LA - eng
KW - existence; uniqueness; Nash-Moser implicit function theorem; subbinomic Fréchet algebras
UR - http://eudml.org/doc/216678
ER -

References

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