Second boundary-value problem for the Lavrent'ev–Bitsadze equation in a rectangular domain with two degeneration lines

For a mixed-type equation, we examine the second boundary-value problem and by using the spectral method prove the uniqueness and existence of solutions. The uniqueness criterion is proved based on the completeness property of the biorthogonal system of functions corresponding to the one-dimensional spectral problem. A solution of the problem is constructed as the sum of a biorthogonal series.