An application of the Nash-Moser theorem to ordinary differential equations in Fréchet spaces
Studia Mathematica, Tome 137 (1999) no. 2, pp. 101-121
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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.
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author = {M. Poppenberg},
title = {An application of the {Nash-Moser} theorem to ordinary differential equations in {Fr\'echet} spaces},
journal = {Studia Mathematica},
pages = {101--121},
publisher = {mathdoc},
volume = {137},
number = {2},
year = {1999},
doi = {10.4064/sm-137-2-101-121},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-137-2-101-121/}
}
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M. Poppenberg. An application of the Nash-Moser theorem to ordinary differential equations in Fréchet spaces. Studia Mathematica, Tome 137 (1999) no. 2, pp. 101-121. doi: 10.4064/sm-137-2-101-121
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