On the anisotropic Wiener-Hopf operator, connected with Helmholtze-Sohrodinger equation

n this article, solvability of one the anisotropic Helmholtz-Shrodinger equation with the boundary conditions of the first and second type is investigated in the upper and lower half –space, (x 5 > 0, x 5 ?0), in 5 dimensions. Solvability of these boundary problems reduces to solvability of RiemanHilbert boundary problem, in general necessary and sufficient conditions for the correctness of the problem in the Sobolev space are presented as well as explicit formulas for a factorization of the Fourier symbol matrix of the one-medium problem. The solvability analysis is based on the factorization problem of some matrix-function.