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An application of the Nash-Moser theorem to ordinary differential equations in Fréchet spaces. (English) Zbl 0949.34052
Summary: 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 $$C^\infty(K)$$, $${\mathcal S}(\mathbb{R}^N)$$, $${\mathcal B}(\mathbb{R}^N)$$, $${\mathcal D}_{L_1}(\mathbb{R}^N)$$, for Köthe sequence spaces, and for the general class of subbinomic Fréchet algebras.

##### MSC:
 34G20 Nonlinear differential equations in abstract spaces 34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations 46A04 Locally convex Fréchet spaces and (DF)-spaces 58C15 Implicit function theorems; global Newton methods on manifolds 46A45 Sequence spaces (including Köthe sequence spaces) 34G10 Linear differential equations in abstract spaces
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