  A Dirichlet-type problem is studied for an equation of even order with
variable coefficients. A criterion for the uniqueness of a solution is given.
The solution is built in the form of a Fourier series. When justifying the
convergence of the series, the problem of small denominators arises. Sufficient
conditions for the separability of the denominator 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 specified derivatives
at the lower boundary of the rectangle.
