ON THE UNIQUE SOLVABILITY OF NONLOCAL IN TIME PROBLEMS CONTAINING THE IONKIN OPERATOR IN THE SPATIAL VARIABLE


КЕҢIСТIК АЙНЫМАЛЫЛЫ ИОНКИН ОПЕРАТОРЫН ҚАМТИТЫН УАҚЫТ БОЙЫНША ЖЕРГIЛIКТI ЕМЕС ЕСЕПТЕРIҢ БIРЕГЕЙ ШЕШIМI ТУРАЛЫ
ОБ ОДНОЗНАЧНОЙ РАЗРЕШИМОСТИ НЕЛОКАЛЬНЫХ ПО ВРЕМЕНИ ЗАДАЧ, СОДЕРЖАЩИХ ОПЕРАТОР ИОНКИНА ПО ПРОСТРАНСТВЕННОЙ ПЕРЕМЕННОЙ
Rasa G.-H.A. Madiyarov M. Mustafina M.
25 December 2025al-Farabi Kazakh State National University

KazNU Bulletin. Mathematics, Mechanics, Computer Science Series
2025#128Issue 435 - 57 pp.

This paper studies a differential equation representing the differences of two operators. One of the operators is generated by linear differential expressions that depend on time. The second operator is the Ionkin operator with respect to the spatial variable. In this paper, the differential operator with respect to time is generated by two-point Birkhoff regular boundary conditions. At the same time, the elliptic operator with respect to the spatial variable does not satisfy the so-called Agmon conditions. Moreover, the operator with respect to the spatial variable is not self-adjoint. In the beginning, the solvability of the problem is proved. In the final part, the uniqueness of the solution is proved. Direct application of the methods of the authors’ previous works to prove the uniqueness of the solution to the problem is quite problematic. However, the authors managed to modify the reasoning of previous works to prove the uniqueness of the solution to the problem.

complete orthonormal systems. , differential-operator equations , elliptic operators , existence of a solution , initial-boundary value problem , operator eigenvalues , solvability of the problem , uniqueness of a solution

Text of the article Перейти на текст статьи

Kabul Education University, Kabul, Afghanistan
Sarsen Amanzholov East Kazakhstan State University, Ust-Kamenogorsk, Kazakhstan

Kabul Education University
Sarsen Amanzholov East Kazakhstan State University

10 лет помогаем публиковать статьи Международный издатель

Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026