This article is cited in 1 paper

Differential inclusions with mean derivatives, having aspherical right-hand sides

Yu. E. Gliklikh

Voronezh State University (Voronezh)

Abstract: On flat $ n $-dimensional torus we study stochastic differential inclusions with mean derivatives, for which the right-hand sides have, generally speaking, not convex (aspherical) values. A subclass of such inclusions is distinguished for which there exists a sequence of $\varepsilon$-approximations, converging point-wise to a Borel measurable selector. On this base a solution existence theorem is obtained.

Keywords: mean derivatives, differential inclusions, aspherical right-hand sides, point-wise convergence, solution existence.

UDC: 517.9

Received: 14.01.2019
Accepted: 11.03.2020

Language: English

DOI: 10.22405/2226-8383-2018-21-2-84-93