An Analogue of the Zhegalov Problem with Data on Internal Characteristics for a Mixed-type Equation with a Singular Coefficient

In this paper, for a mixed type equation with a singular coefficient, a boundary value problem of Zhegalev type is studied with data on internal characteristics and a Frankl type condition on the type change line. Based on the extremum principle, the uniqueness theorem is proven. Using the theories of singular integral equations with a shift and the Wiener–Hopf equations, the existence of a solution to the problem posed is proven.