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Existence theorems for the solutions of differential inclusions. (Théorème d’existence de solutions d’inclusions différentielles.) (French) Zbl 0834.34021
Granas, Andrzej (ed.) et al., Topological methods in differential equations and inclusions. Proceedings of the NATO Advanced Study Institute and séminaire de mathématiques supérieures on topological methods in differential equations and inclusions, Montréal, Canada, July 11-22, 1994. Dordrecht: Kluwer Academic Publishers. NATO ASI Ser., Ser. C, Math. Phys. Sci. 472, 51-87 (1995).
Summary: 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.
For the entire collection see [Zbl 0829.00024].

MSC:
34A60 Ordinary differential inclusions
47H10 Fixed-point theorems
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