%0 Journal Article
%T On Peano's theorem in Banach spaces
%A Petr H¨˘jek
%A Michal Johanis
%J Mathematics
%D 2009
%I arXiv
%X 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.
%U http://arxiv.org/abs/0911.4860v1