A Problem with an Analogue of the Bitsadze–Samarskii Condition on the Segment of Degeneracy and an Internal Segment Parallel to It in the Domain for a Certain Class of Degenerate Hyperbolic Equations

For the equation $$ - {{( - y)}^{m}}{{u}_{{xx}}} + {{u}_{{yy}}} - \frac{m}{{2y}}{{u}_{y}} = 0$$ in the characteristic triangle, the unique solvability of the problem with the Bitsadze–Samarsky condition is proven on the segment of degeneracy of the equation and on an internal segment parallel to it and lying inside the domain.