English

A Lipschitz condition along a transversal foliation implies local uniqueness for ODEs

Classical Analysis and ODEs 2018-01-08 v1

Abstract

We prove the following result: if a continuous vector field FF is Lipschitz when restricted to the hypersurfaces determined by a suitable foliation and a transversal condition is satisfied at the initial condition, then FF determines a locally unique integral curve. We also present some illustrative examples and sufficient conditions in order to apply our main result.

Cite

@article{arxiv.1801.01724,
  title  = {A Lipschitz condition along a transversal foliation implies local uniqueness for ODEs},
  author = {J. Ángel Cid and F. Adrián F. Tojo},
  journal= {arXiv preprint arXiv:1801.01724},
  year   = {2018}
}
R2 v1 2026-06-22T23:37:19.869Z