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arXiv · 1801.01724

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

J. Ángel Cid·F. Adrián F. Tojo
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Abstract

We 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 result.

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J. Ángel Cid, F. Adrián F. Tojo. 2018-01-05. A Lipschitz condition along a transversal foliation implies local uniqueness for ODEs. https://arxiv.org/abs/1801.01724

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