English

Optimal version of the Picard-Lindel\"of theorem

Classical Analysis and ODEs 2021-10-05 v1

Abstract

Consider the differential equation y=F(x,y)y'=F(x,y). We determine the weakest possible upper bound on F(x,y)F(x,z)|F(x,y)-F(x,z)| which guarantees that this equation has for all initial values a unique solution, which exists globally.

Keywords

Cite

@article{arxiv.2110.00999,
  title  = {Optimal version of the Picard-Lindel\"of theorem},
  author = {Jan-Christoph Schlage-Puchta},
  journal= {arXiv preprint arXiv:2110.00999},
  year   = {2021}
}