Topological approach to random diferential inclusions

Year 2020, Volume: 3 Issue: 4, 196 - 206, 30.12.2020

Lech Górniewicz

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.

Keywords

random operators,, multivalued mappings,, fixed points, topological essentiality, topological degree, differential inclusions

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