### 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 |
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Pages (from-to) | 108-115 |

Number of pages | 8 |

Journal | Mathematical Notes |

Volume | 62 |

Publication status | Published - 1997 |

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## Cite this

Shkarin, S. (1997). Counterexample to Peano's theorem in infinite-dimensional F '-spaces.

*Mathematical Notes*,*62*, 108-115.