Keldysh type problem with an integral condition for two-dimensional $B$-hyperbolic equation

In a rectangular domain, a nonlocal problem with insufficient boundary conditions and an integral condition of the first kind is studied for a two-dimensional hyperbolic equation with the Bessel operator. The uniqueness and existence theorems are proved for this problem by the method of spectral analysis. The solution to the problem is constructed in the form of a Fourier–Bessel series, the problem of small denominators is resolved. Estimates for the initial functions are obtained and the convergence of the series in the class of regular solutions is proved.