Topological approach to random diferential inclusions

Abstract

In the present paper random multivalued admissible operators are considered. First for such operators we shall formulate the following topological results: Schauder-type Fixed Point Theorems, Leray?Schauder Alternative, Granas Continuation Method and Topological Degree. Next these problems will be transformed to the existence problems, periodic problems and implicit problems for random di?erentuial inclusions. Let us remark that this paper constitute a summary and complement of the following earlier papers: [2], [3], [5], [6], [10], [11], [14] and [15]. This work can be considered as an advanced survey with some new results: mainly concerning the theory of random di?erential inclusions. We believe that this paper will be useful for mathematiciants and students intrested in topological methods of nonconvex analysis.