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

Abstract

In this paper, we study a Dirichlet type problem in a rectangular domain for an equation of the Lavrentiev-Bitsadze type of high order type. The necessary and sufficient conditions for the uniqueness of the solution of the problem are obtained by 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.