Topological approach to random dierential 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, LeraySchauder Alternative, Granas Continuation Method and Topological Degree. Next these problems will be transformed to the existence problems, periodic problems and implicit problems for random dierentuial 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 dierential inclusions. We believe that this paper will be useful for mathematiciants and students intrested in topological methods of nonconvex analysis.