This article is cited in 13 papers

Some results on solvability of ordinary linear differential equations in locally convex spaces

S. A. Shkarin

M. V. Lomonosov Moscow State University

Abstract: Let $\Gamma$ be the class of sequentially complete locally convex spaces such that an existence theorem holds for the linear Cauchy problem $\dot x=Ax$, $x(0)=x_0$, with respect to functions $x\colon\mathbf R\to E$. It is proved that if $E\in\Gamma$, then $E\times\mathbf R^A\in\Gamma$ for an arbitrary set $A$. It is also proved that a topological product of infinitely many infinite-dimensional Fréchet spaces, each not isomorphic to $\mathbf R^\infty$, does not belong to $\Gamma$.

UDC: 517.9

MSC: Primary 34A10, 34G10; Secondary 46A05

Received: 22.06.1989

 English version: Mathematics of the USSR-Sbornik, 1992, 71:1, 29–40

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