Cid, José ÁngelFernández Tojo, Fernando Adrián2019-10-262019-10-262018Cid, J., & Tojo, F. (2018). A Lipschitz condition along a transversal foliation implies local uniqueness for ODEs. Electronic Journal Of Qualitative Theory Of Differential Equations, (13), 1-14. doi: 10.14232/ejqtde.2018.1.13http://hdl.handle.net/10347/19946We prove the following result: if a continuous vector field F is Lipschitz when restricted to the hypersurfaces determined by a suitable foliation and a transversal condition is satisfied at the initial condition, then F determines a locally unique integral curve. We also present some illustrative examples and sufficient conditions in order to apply our main resultengThis is an open access article distributed under the Creative Commons Attribution License (CC BY 4.0)http://creativecommons.org/licenses/by/4.0/UniquenessLipschitz conditionFoliationModulus of continuityRotation formulajournal article10.14232/ejqtde.2018.1.131417-3875open access