On the Keldysh problem for mixed type equation with two singular lines

In this paper we consider the Keldysh problem in rectangular domain for mixed type equation with two singular coefficients. We prove the criterion of Keldysh problem solution uniqueness on the basis of corresponding spectral problem eigenfunctions system completeness. We construct the Keldysh problem solution as the sum of eigenfunctions series. We obtained separation from zero estimates of small denominators. We prove the existence theorem using this estimates.