A coefficient determination in nonlocal problem for Boussinesq type integro-differential equation with degenerate kernel

In the three-dimensional domain a Boussinesq type linear integro-differential equation of the fourth order with a restore coefficient and a degenerate kernel is considered. The solution of this integro-differential equation is considered in the class of continuously differentiable functions. First, we study the classical solvability of a nonlocal direct boundary value problem for the considered Boussinesq integro-differential equation with a parameter in the integral term. The method of separation of variables and the method of a degenerate kernels are used. A countable system of algebraic equations is obtained. The solution of this algebraic system of equations for regular values of the spectral parameter in the integral term of a given equation allows us to construct a solution of a non-local direct boundary value problem for an integro-differential equation in the form of a Fourier series. A criterion for the unique solvability of a direct boundary value problem is established for fixed values of the restore function...