Nonlocal A. A. Dezin's problem for Lavrent'ev–Bitsadze equation

For mixed type equation $u_{xx}+(\operatorname{sgn}y)u_{yy}=0$ in the rectangular domain by the method of spectral analysis we establish a criterion of uniqueness of the solution to a problem with the periodicity conditions on the variable $x$, nonlocal condition and the boundary condition. The solution is constructed as the sum of a series in eigenfunctions corresponding to one-dimensional spectral problem. In the substantiation of convergence of series the problem of small denominators arises. Under certain conditions on the parameters and the given functions we prove uniform convergence of the constructed series and stability of the solution from the set of these functions.