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In this paper we study the solutions of the stationary Schrödinger equation on unbounded domains of Riemannian manifolds with noncompact boundary. For the proper formulation of the boundary value problems we use an approach based on the introduction of equivalent functions class. We obtain sufficient conditions for solvability of some boundary value problems on such manifolds. AMS Subject Classification: 58J32

ON SOLVABILITY OF BOUNDARY VALUE PROBLEMS FOR SOLUTIONS OF THE STATIONARY SCHRODINGER EQUATION ON UNBOUNDED DOMAINS OF RIEMANNIAN MANIFOLDS