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

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### Abstract

Let $E$ be a nonnormable Frechet space, and let $E'$ be the space of all continuous linear functionals on $E$ in the strong topology. A continuous mapping $f : E' \to E'$ such that for any $t_0\in R$ and $x_0\in E'$, the Cauchy problem $\dot x= f(x)$, x(t_0) = x_0\$ has no solutions is constructed.
Original language English 108-115 8 Mathematical Notes 62 Published - 1997