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

Poppenberg, M.

Poppenberg, M.

Studia Mathematica, Tome 133 (1999), p. 101-121 / Harvested from The Polish Digital Mathematics Library

Résumé

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 $C^{\infty} (K)$ , $S (ℝ^{N})$ , $B (ℝ R^{N})$ , $D_{L_{1}} (ℝ^{N})$ , for Köthe sequence spaces, and for the general class of subbinomic Fréchet algebras.

Publié le : 1999-01-01

Zbl 0949.34052

EUDML-ID : urn:eudml:doc:216678

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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},
     volume = {133},
     year = {1999},
     pages = {101-121},
     zbl = {0949.34052},
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Poppenberg, M. An application of the Nash-Moser theorem to ordinary differential equations in Fréchet spaces. Studia Mathematica, Tome 133 (1999) pp. 101-121. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv137i2p101bwm/

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