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
[Conditions fines d'unicité pour les équations différentielles ordinaires autonomes en dimension 1]

Présenté par : 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.

Résumé
Abstract

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.

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.

Reçu le : 2018-05-18
Accepté le : 2018-07-18
Publié le : 2018-07-31

DOI : 10.1016/j.crma.2018.07.008

Affiliations des auteurs :

Ulrik Skre Fjordholm ¹

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

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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/

Bibliographie
Cité par

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