On an anisotropic boundary problem of diffraction with first and second type boundary conditions

In the present paper solvability of a class of boundary problems associated with the anisotropic Helmholtz-Shrodinger equation in the upper and lower semiplanes of Sobolev spaces is studied. The first and second type boundary conditions are assumed to hold on the line $\ y=0$. Solvability of these boundary problems reduces to solvability of Riman-Hilbert boundary problem. The solvability analysis is based on the factorization problem of some matrix-function.