This article is cited in 9 papers

Counterexample to Peano's theorem in infinite-dimensional $F'$-spaces

S. A. Shkarin

M. V. Lomonosov Moscow State University

Abstract: Let $E$ be a nonnormable Fréchet space, and let $E'$ be the space of all continuous linear functionals on $E$ in the strong topology. A continuous mapping $f\colon E'\to E'$ such that for any $t_0\in\mathbb R,x_0\in E'$, the Cauchy problem $\dot x=f(x)$, $x(t_0)=x_0$ has no solutions is constructed.

UDC: 517

Received: 25.01.1995
Revised: 01.12.1995

DOI: 10.4213/mzm1596

 English version: Mathematical Notes, 1997, 62:1, 108–115

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