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 is Lipschitz when restricted to the hypersurfaces determined by a suitable foliation and a transversal condition is satisfied at the initial condition, then 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}
}