Fixed Point Differential Inclusin Multifunction Measurable Selection Pseudo-Lipchitzness
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Serdica Mathematical Journal, Vol. 37, No 1, (2011), 1p-8p
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.