On Peano's theorem in Banach spaces
Classical Analysis and ODEs
2009-11-26 v1 Functional Analysis
Abstract
We show that if 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 such that the autonomous differential equation has no solution at any point.
Cite
@article{arxiv.0911.4860,
title = {On Peano's theorem in Banach spaces},
author = {Petr Hájek and Michal Johanis},
journal= {arXiv preprint arXiv:0911.4860},
year = {2009}
}