Nonlocal problem for a mixed type differential equation in rectangular domain

In the article the questions of solvability and construction of the solution of nonlocal mixed value problem for a homogeneous mixed type differential equa tion are considered. The spectral method based on the separation of variables is used. A criterion for a single-valued solvability of the considered problem is installed. Under this criterion the single-valued solvability of the problem is proved. The existence of problem solutions in the case of uniqueness failure is studied, also.