An application of the Nash-Moser theorem to ordinary differential equations in Fréchet spaces
Volume 137 / 1999
Studia Mathematica 137 (1999), 101-121
DOI: 10.4064/sm-137-2-101-121
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.
