Vol 68, No 2 (2022)
- Year: 2022
- Articles: 3
- URL: https://journals.rudn.ru/CMFD/issue/view/1550
- DOI: https://doi.org/10.22363/2413-3639-2022-68-2
Full Issue
Articles
Stochastic Equations and Inclusions with Mean Derivatives and Their Applications
Abstract
This work is a detailed presentation of the results, mainly obtained in recent years by the author and his school of the research of mean derivatives of random processes, stochastic equations and inclusions with mean derivatives, as well as their applications in various mathematical disciplines, mainly in mathematical physics. In addition, the work contains introductory material on mean derivatives by E. Nelson, who introduced this concept in the 60s of the XXs century, the results of other researchers on this topic, and preliminary concepts from various areas of mathematics used in this work.


On the Completeness of Eigenfunctions of One 5th-Order Differential Operator
Abstract
In this paper, we fully solve the problem of the completeness of the eigenfunctions of an ordinary 5th-order differential operator in the space of square-summable functions on the segment [0, 1] generated by the simplest differential expression



Asymptotic Behavior of the Solution for One Class of Nonlinear Integral Equations of Hammerstein Type on the Whole Axis
Abstract
A class of nonlinear integral equations on the whole axis with a noncompact integral operator of Hammerstein type is investigated. This class of equations has applications in various fields of natural science. In particular, such equations are found in mathematical biology, in the kinetic theory of gases, in the theory of radiation transfer, etc. The existence of a nonnegative nontrivial and bounded solution is proved. The asymptotic behavior of the constructed solution on ±∞ is studied. In one important special case, the uniqueness of the constructed solution in a certain weighted space is established. At the end of the work, specific applied examples of the equations under study are given.

