Boundary-value problem with nonlocal integral condition for mixed-type equations with degeneracy on the transition line

For an elliptic-hyperbolic type equation, the boundary-value problem with nonlocal Samarskii–Ionkin condition in a rectangular domain is solved. Using the spectral analysis method, a uniqueness criterion is established and the existence theorem for the solution of the problem is proved. The solution of the problem is constructed as the sum of a biorthogonal series.