Abstract:
In this work, the classical method of guiding functions due to M.A. Krasnoselskii and A.I. Perov is extended to the case of nonsmooth integral guiding functions for random functional-differential inclusions. The paper deals with a periodic problem for a random functional-differential inclusion, the right-hand side of which is a u-multimap satisfying conditions of sublinear growth. To solve this problem, we use the theory of the topological coincidence degree for a pair of mappings consisting of a linear Fredholm operator of zero index and a random multivalued mapping. As an example, we consider the solvability of a periodic problem for a random gradient functional differential inclusion. Acknowledgements This research was supported by the Ministry of Education of the Russian Federation within the framework of the state task in the field of science (topic number QRPK-2023-0002).
Keywords:random Multi-Reflection, random Functional Differential Inclusion, random u-Operator, random Solution, random Nonsmooth Strict Integral Guide Function, generalized Clarke Derivative, generalized Clarke Gradient, random Topological Index, random Topological Degree.
