Contemporary Mathematics. Fundamental DirectionsContemporary Mathematics. Fundamental DirectionsСовременная математика. Фундаментальные направления2413-36392949-0618Peoples’ Friendship University of Russia named after Patrice Lumumba (RUDN University)4390310.22363/2413-3639-2025-71-1-1-17SPXFTPArticlesСтатьиResearch ArticleOn the nonlocal boundary value problem for the elliptic differential equations with integral type Samarskii-Ionkin conditionsО нелокальной краевой задаче для эллиптических дифференциальных уравнений с условиями Самарского-Ионкина интегрального типаAshyralyevAllaberenАшыралыевАллаберенallaberen.ashyralyev@eng.bau.edu.trHamadAymanХамадАйманayman.hamad@uob.edu.lyBahcesehir UniversityRUDN UniversityРоссийский университет дружбы народовInstitute of Mathematics and Mathematical ModelingИнститут математики и математического моделированияUniversity of Benghazi15122025711Nonlocal and nonlinear problemsНелокальные и нелинейные задачи11721042025Copyright ©; 2025, Ashyralyev A., Hamad A.Copyright ©; 2025, Ашыралыев А., Хамад А.2025Ashyralyev A., Hamad A.Ашыралыев А., Хамад А.https://creativecommons.org/licenses/by-nc/4.0https://journals.rudn.ru/CMFD/article/view/43903

The present paper is devoted to the study of the abstract nonlocal boundary value problem with integral type Samarskii–Ionkin conditions for the differential equation of elliptic type \[\hspace{-6em} -u''(t)+Au(t)=f(t)\quad (0\leq t\leq T),\quad u\left( 0\right) =\varphi,\quad u'\left( 0\right) =u'\left( T\right) +\int\limits_{0}^{T}\alpha \left( s\right) u(s)ds+\psi.\quad\] in an arbitrary Banach space \(E\) with the positive operator \(A\). The well-posedness of this problem in various Banach spaces is established. In applications, theorems on the well-posedness of several nonlocal boundary value problems for elliptic equations with integral type Samarskii–Ionkin conditions are proved.

Настоящая работа посвящена исследованию абстрактной нелокальной краевой задачи с условиями Самарского—Ионкина интегрального типа для дифференциального уравнения эллиптического типа \[\hspace{-6em} -u''(t)+Au(t)=f(t)\quad (0\leq t\leq T),\quad u\left( 0\right) =\varphi,\quad u'\left( 0\right) =u'\left( T\right) +\int\limits_{0}^{T}\alpha \left( s\right) u(s)ds+\psi\] в произвольном банаховом пространстве \(E\) с положительным оператором \(A.\) Устанавливается корректность этой задачи в различных банаховых пространствах. В приложениях доказываются теоремы о корректности ряда нелокальных краевых задач для эллиптических уравнений с условиями Самарского—Ионкина интегрального типа.

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