On Differential Inclusions with Unbounded Right-Hand Side

2000 Mathematics Subject Classification: 58C06, 47H10, 34A60.

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.