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SAMM - Statistique, Analyse, Modélisation Multidisciplinaire |  |
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SAMM - Statistique, Analyse, Modélisation Multidisciplinaire | |
| HAL : hal-00707819, version 1 |
| DOI : 10.1090/S0002-9939-2012-11154-2 |
| Fiche détaillée |  Récupérer au format |
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| Proceedings of the American Mathematical Society, 140 (2012) 2825-2834 |
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| On the nonexistence of purely Stepanov almost-periodic solutions of ordinary differential equations |
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| Jan Andres 1Denis Pennequin 1 |
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| (2012) |
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| It is shown that in uniformly convex Banach spaces, Stepanov almost-periodic functions with Stepanov almost-periodic derivatives are uniformly almost-periodic in the sense of Bohr. This in natural situations yields, jointly with the derived properties of the associated Nemytskii operators, the nonexistence of purely (i.e.nonuniformly continuous) Stepanov almost-periodic solutions of ordinary differential equations. In particular, the existence problem of such solutions, considered in a series of five papers of Z. Hu and A. B. Mingarelli, is answered in a negative way. |
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| 1 : | Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne) (SAMM) |
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Université Paris I - Panthéon-Sorbonne |
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| Domaine | : | Mathématiques/Analyse classique Mathématiques/Systèmes dynamiques |
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| Stepanov almost-periodic solutions – Nemytskii operators – ordinary differential equations – nonexistence results |
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| hal-00707819, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00707819 | |
| oai:hal.archives-ouvertes.fr:hal-00707819 | |
| Contributeur : Denis Pennequin | |
| Soumis le : Mercredi 13 Juin 2012, 15:27:02 | |
| Dernière modification le : Mardi 26 Février 2013, 22:11:19 | |
