A nonlocal boundary value problem for a system of partial differential equations with loading is investigated. Such boundary value problems are encountered in applications in the form of a mathematical model, including a differential model of real physical, biological, ecological and other processes. Loaded differential equations describe the dynamics of a closed population, processes occurring in a continuous medium, etc.

Loaded differential equations arise when replacing the integral term of integro-differential equations, as well as when constructing an approximate solution to a system of integro-differential equations. Of considerable interest are boundary value problems with nonlocal constraints for loaded differential equations. A significant number of works are devoted to the construction of constructive methods for studying problems for some classes of loaded differential equations. As is known, conditions for the existence and uniqueness of a solution to boundary value problems for such equations are obtained by various methods.

For a boundary value problem with a nonlocal condition for a second-order partial differential equation, the issue of unique solvability is studied. Equivalence of solutions of a nonlocal boundary value problem for a loaded partial differential equation and a boundary value problem with a nonlocal condition for a first-order partial differential equation and a connecting integral relation is established.

An algorithm for finding a solution to such boundary value problems is proposed.

ABDIKALIKOVA G.А.

Candidate of Physical and Mathematical Sciences, Associate Professor, K. Zhubanov Aktobe Regional University, Aktobe, Kazakhstan

Е-mail: agalliya@mail.ru; https://orcid.org/0000-0001-6280-4168

SHAKIMOV YE.Е.

Master's student, K. Zhubanov Aktobe Regional University, Aktobe, Kazakhstan

Е-mail: eron1997@mail.ru; https://orcid.org/0009-0001-0000-8729

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