English

On Peano's theorem in Banach spaces

Classical Analysis and ODEs 2009-11-26 v1 Functional Analysis

Abstract

We show that if XX 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 ⁣:XXf\colon X\to X such that the autonomous differential equation x=f(x)x'=f(x) has no solution at any point.

Keywords

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}
}
R2 v1 2026-06-21T14:15:58.811Z