On a Boundary-Value Problem for a Fourth-Order Partial Integro-Differential Equation with Degenerate Kernel

In this paper, the classical solvability of a nonlocal boundary-value problem for a three-dimensional, homogeneous, fourth-order, pseudoelliptic integro-differential equation with degenerate kernel is proved. The spectral Fourier method based on the separation of variables is used and a countable system of algebraic equations is obtained. A solution is constructed explicitly in the form of a Fourier series. The absolute and uniform convergence of the series obtained and the possibility of termwise differentiation of the solution with respect to all variables are justified. A criterion of unique solvability of the problem considered is ascertained.