On a Navier-type boundary value problem for a nonlocal analogue of a polyharmonic equation with multiple involution

This paper is devoted to research of the solvability of a Navier-type boundary value problem for a nonlocal analogue of a polyharmonic equation. Nonlocal operators in the equation and boundary conditions are introduced using mappings with the involution property. Conditions for the existence and uniqueness of a solution are established for the problem under consideration. By employing the Green's function for the classical polyharmonic operator, an integral representation of the solution to the nonlocal problem is obtained. An analysis of the corresponding spectral problem is also performed: explicit expressions for the eigenfunctions and eigenvalues are obtained. A theorem on the completeness of the system of eigenfunctions in the space L2 is proved.