Sharp uniqueness conditions for one-dimensional, autonomous ordinary differential equations

Ulrik Skre Fjordholm

doi:10.1016/j.crma.2018.07.008

Ordinary differential equations

Sharp uniqueness conditions for one-dimensional, autonomous ordinary differential equations

Presented by: the Editorial Board

Ulrik Skre Fjordholm ¹

¹ Department of Mathematics, University of Oslo, Postboks 1053 Blindern, 0316 Oslo, Norway

Comptes Rendus. Mathématique, Volume 356 (2018) no. 9, pp. 916-921.

Abstract
Résumé

We give two conditions that are necessary and sufficient for the uniqueness of Filippov solutions to scalar, autonomous ordinary differential equations with discontinuous velocity fields. When only one of the two conditions is satisfied, we give a natural selection criterion that guarantees uniqueness of the solution.

Nous donnons deux conditions nécessaires et suffisantes pour l'unicité des solutions de Filippov des équations différentielles ordinaires autonomes scalaires, avec champs de vitesse discontinus. Lorsqu'une seule de ces deux conditions est satisfaite, nous donnons un critère naturel sélectionnant une unique solution.

Received: 2018-05-18
Accepted: 2018-07-18
Published online: 2018-07-31

DOI: 10.1016/j.crma.2018.07.008

Author's affiliations:

Ulrik Skre Fjordholm ¹

¹ Department of Mathematics, University of Oslo, Postboks 1053 Blindern, 0316 Oslo, Norway

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     title = {Sharp uniqueness conditions for one-dimensional, autonomous ordinary differential equations},
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Ulrik Skre Fjordholm. Sharp uniqueness conditions for one-dimensional, autonomous ordinary differential equations. Comptes Rendus. Mathématique, Volume 356 (2018) no. 9, pp. 916-921. doi : 10.1016/j.crma.2018.07.008. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2018.07.008/

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