On the Conditions for the Solvability of Boundary-Value Problems for Higher-Order Equations with Discontinuous Coefficients

A Dirichlet-type problem for an equation of high even order with discontinuous coefficients is studied. A criterion for the uniqueness of the solution is given. The solution in the form of the Fourier series in the eigenfunctions of the one-dimensional problem is constructed. The problem of small denominators arises when justifying the convergence of the series. Sufficient conditions for the denominator to be distinct from zero are obtained. It is shown that the solvability of the problem is influenced not only by the dimension of the rectangle, but also by the orders of the given derivatives at the lower boundary of the rectangle.