On the Keldysh Problem for a Mixed-Type Equation with Two Singular Lines

The Keldysh problem is considered in a rectangular domain for a mixed-type equation with two perpendicular singularity lines. The uniqueness of the solution of this problem is established from the completeness of the system of eigenfunctions of the corresponding spectral problem. The solution is constructed as a series in terms of the system of eigenfunctions. The convergence of this series is substantiated through estimates made for the separability from zero of small denominators. These estimates have been used to prove an existence theorem for a solution to the Keldysh problem.