Keldysh problem for mixed type equation with strong characteristic degeneration and singular coefficient

Abstract

We study a mixed-type equation of the second kind with a singular coefficient. With the help of the spectral analysis method we establish a uniqueness criterion for a solution of the problem with incomplete boundary data. The solution represents the sum of the Fourier–Bessel series. The substantiation of its uniform convergence is based on an estimate of the separation from zero of the small denominator with the corresponding asymptotic behavior. This allows us to prove the convergence of the series in the class of regular solutions.