This article is cited in 11 papers

Picard's theorem for ordinary differential equations in locally convex spaces

S. G. Lobanov

Moscow State Automobile and Road Technical University

Abstract: A class of infinite-dimensional Frechet spaces is constructed, including certain subspaces of $C^\infty[-1,1]$, in which Picard's theorem on solvability of an ODE with smooth right-hand side is valid in the usual formulation. Every continuous linear operator on these spaces has an exponential.

UDC: 517.9

MSC: Primary 34A12, 34G20; Secondary 46A04, 46A08

Received: 23.10.1991

 English version: Russian Academy of Sciences. Izvestiya Mathematics, 1993, 41:3, 465–487

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