Problem with displacement conditions on internal characteristics and the Frankl condition on a segment of the degeneration line for the Gellerstedt equation with a singular coefficient

We study the well-posedness of a problem with displacement conditions on internal characteristics and an analog of the Frankl condition on a segment of the degeneration line for the Gellerstedt equation with a singular coefficient. The uniqueness of a solution is proved with the use of an extremum principle. The proof of the existence uses the method of integral equations.