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