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Théorèmes d’existence de solutions d’inclusions différentielles

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Topological Methods in Differential Equations and Inclusions

Part of the book series: NATO ASI Series ((ASIC,volume 472))

Résumé

Dans ce texte, on présente quelques applications de méthodes topologiques permettant d’obtenir l’existence de solutions d’inclusions differentielles ordinaires. Trois types de fonctions multivoques sont distingués et un principe general d’existence de solutions est etabli pour chacun d’eux. Des résultats sont obtenus pour des systèmes d’inclusions différentielles du second ordre et pour des inclusions differentielles dans des espaces de Banach. Les principaux théorèmes obtenus découlent soit de théorèmes de point fixe, soit de la théorie de la transversalité topologique pour des operateurs compacts ou con-tractants, univoques ou multivoques.

Abstract

In this text, we present applications of topological methods to ordinary differential inclusions. Three types of multivalued functions are considered and a general existence principle is established for each of them. Results are obtained for second order systems of differential inclusions, and for differential inclusions in Banach spaces. Main theorems rely either on fixed point theorems or on topological transversality theories for compact or contractive, univalued or multivalued operators.

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Author information

Authors and Affiliations

  1. Département de mathématiques et de statistique, Université de Montréal, C.P. 6128, succ. Centre-ville, Montréal, Qué., H3C 3J7, Canada

    Marlène Frigon

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  1. Marlène Frigon
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Editors and Affiliations

  1. Département de mathématiques et de statistique, Université de Montréal, Montréal, Québec, Canada

    Andrzej Granas , Marlène Frigon  & Gert Sabidussi ,  & 

  2. Faculty of Mathematics and Informatics, Nicholas Copernicus University, Toruń, Poland

    Andrzej Granas

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Frigon, M. (1995). Théorèmes d’existence de solutions d’inclusions différentielles. In: Granas, A., Frigon, M., Sabidussi, G. (eds) Topological Methods in Differential Equations and Inclusions. NATO ASI Series, vol 472. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0339-8_2

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  • DOI: https://doi.org/10.1007/978-94-011-0339-8_2

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4150-8

  • Online ISBN: 978-94-011-0339-8

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