Keldysh problem for Pulkin’s equation in a rectangular domain

In this article for the mixed type equation with a singular coefficient Keldysh problem of incomplete boundary conditions is studied. On the basis of property of completeness of the system of own functions of one-dimensional spectral problem the criterion of uniqueness is established. The solution is constructed as the summary of Fourier–Bessel row. At the foundation of the uniform convergence of a row there is a problem of small denominators. Under some restrictions on these tasks evaluation of separation from zero of a small denominator with the corresponding asymptotics was found, which helped to prove the uniform convergence and its derivatives up to the second order inclusive, and the existence theorem in the class of regular solutions.