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arXiv · 0911.4860

On Peano's theorem in Banach spaces

Petr Hájek·Michal Johanis
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Abstract

We show that if $X$ is an infinite-dimensional separable Banach space (or more generally a Banach space with an infinite-dimensional separable quotient) then there is a continuous mapping $f\colon X\to X$ such that the autonomous differential equation $x'=f(x)$ has no solution at any point.

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Petr Hájek, Michal Johanis. 2009-11-25. On Peano's theorem in Banach spaces. https://arxiv.org/abs/0911.4860

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