On Peano's theorem in Banach spaces

Details On Peano's theorem in Banach spaces On Peano's theorem in Banach spaces

2009-11-25

arxiv.org/abs/0911.4860v1

Mathematics

Classical Analysis and ODEs

Scientific paper

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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