On a boundary value problem for a high order mixed type equation

In this paper, we study a Dirichlet type problem for a Lavrentiev–Bitsadze type equation of high order type in a rectangular domain. The necessary and sufficient conditions for the uniqueness of the problem solution are obtained by using the spectral method. The solution is constructed in the form of a series of eigenfunctions. When substantiating the convergence of a series, the problem of «small» denominators arises. Sufficient conditions are obtained for the separability of the «small» denominator from zero.