Application of the Nonsmooth Integral Guiding Functions Method for Studying of the Periodic Problem for Random Functional Differential Inclusions with a Perturbed Right-Hand Side
DOI:
https://doi.org/10.52575/2687-0959-2026-58-3-262-269Keywords:
Random Multivalued Map, Random Integral Guiding Function, Random Functional Differential Inclusion with a Perturbed Right-Hand Side Extended, Multivalued Superposition MultimapAbstract
In this work, based on the theory of random fixed points and random topological degree theory for random multivalued mappings, new topological and geometrical methods are presented for investigating of the periodic problem for a random functional differential inclusion with a perturbed right-hand side, represented as the sum of a random upper semicontinuous multivalued map and a random continuous map with respect to the collection of variables, where one of the variables is represented as a function. An extended multivalued superposition operator is constructed for the given problem. The method of random nonsmooth integral guiding functions is applied to study the posed problem. The existence theory of a random periodic solution of the posed problem is formulated and proved.
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