Geodesic
On Differential Inclusions with Unbounded Right-Hand Side
Serdica Mathematical Journal, Tome 37 (2011) no. 1, pp. 1-8.

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The classical Filippov's Theorem on existence of a local trajectory of the differential inclusion [dot x](t) О F(t,x(t)) requires the right-hand side F(·,·) to be Lipschitzian with respect to the Hausdorff distance and then to be bounded-valued. We give an extension of the quoted result under a weaker assumption, used by Ioffe in [J. Convex Anal. 13 (2006), 353-362], allowing unbounded right-hand side.
Keywords: Fixed Point, Differential Inclusin, Multifunction, Measurable Selection, Pseudo-Lipchitzness 
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Benahmed, S. On Differential Inclusions with Unbounded Right-Hand Side. Serdica Mathematical Journal, Tome 37 (2011) no. 1, pp. 1-8. http://geodesic.mathdoc.fr/item/SMJ2_2011_37_1_a0/