Abstract
ABSTRACT This article examines the unique solvability of a boundary value problem for hyperbolic systems under periodic conditions. To solve the stated problem, the Dzhumabaev method is employed, which transforms the original boundary value problem into an equivalent multipoint boundary value problem for ordinary differential equations with parameters, incorporating both initial and additional boundary conditions. Furthermore, the study establishes a connection between the unique solvability of the original problem and the invertibility of the matrix . Recurrent relations for determining the elements of the inverse matrix are also derived.