Problem with a Periodicity Condition for an Equation of the Mixed Type with Strong Degeneration

Abstract

A boundary value problem for a mixed-type equation of the second kind is studied in a rectangular domain. The periodicity condition is posed on the lateral sides of the rectangle, and the values of the desired function are prescribed on the bases of the rectangle. Transmission conditions are specified on the singular line. The solution is constructed as the sum of a series. Sufficient conditions on the given functions and the rectangular domain ensuring the existence of a solution are found. A uniqueness criterion is established.