S.A. Hosseini Matikolai, H. Jafari, Roshanak Lotfikar / TJMCS Vol. 4 No. 3 (2012) 301 - 309 301 Available online at http:/ / www.TJMCS.com The Journal of Mathematics and Computer Science Vol. 4 No.3 (2012) 301 - 309 On the anisotropic Wiener-Hopf operator, connected with Helmholtze-Sohrodinger equation S.A. Hosseini Matikolai 1 , H. Jafari 2 , Roshanak Lotfikar 3 1- Department of Mathematics, Yerevan State University, Yerevan, Armenia seyedm895@yahoo.com 2- Department of Mathematics, University of Mazandaran, Babolsar, Iran jafari@umz.ac.ir 3- Islamic Azad University Ilam branch rlotfikar@yahoo.com Received: February 2012, Revised: May 2012 Online Publication: July 2012 Abstract In 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, (x5>0, x50), in 5 dimensions. Solvability of these boundary problems reduces to solvability of Rieman- Hilbert 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. 1 Keywords: Helmholtz-Shrodinger equation, Factorization of matrix-function, Boundary value problem, Wiener- Hopf equation. 1. Introduction Was a certain class of diffraction problems leading investigated to simultaneous 22 systems of Wiener-Hopf equations. First the classical Wiener- Hopf technique was represented by Noble [1]. 1 2000 Mathematics subject classifications: 47A68,47A70 The J ournal of M athematics and C omputer S cience