On nonlocal integro-differential boundary value problems of multidimensional pseudohyperbolic equations

The solvability of an initial-boundary value problem with a boundary condition connecting the values of a solution or the conormal derivative of a solution with values of some integral operator on a solution for linear integral-differential pseudohyperbolic equations is studied. Existence and uniqueness theorems of regular solutions are proven. The systematic study of nonlocal boundary value problems of finding periodic solutions to elliptic equations began with the articles by A. V. Bitsadze and A. A. Samarskii (1969). There are also investigations of third-order integral-differential pseudoparabolic equations with an integral condition on the lateral boundary (2024). A major contribution to the development of the theory of nonlocal problems for differential equations of various classes was made in the monographs by A. L. Skubachevsky (1997), A. M. Nakhushev (2006, 2012), and A. I. Kozhanov (2024).