Abstract
We study the solutions of the stationary Schrödinger equation in unbounded domains on Riemannian manifolds with noncompact boundary. Our approach to the statement of boundary value problems is based on the notion of a class of equivalent functions. We obtain sufficient conditions for the solvability of boundary value problems and prove the solvability of the Dirichlet problem on the cone of a model manifold with continuous boundary data on the boundary.
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Korol’kov, S.A. and Korol’kova, E.S., Boundary Value Problems for Harmonic Functions in Unbounded Domains of Riemannian Manifolds, Vestn. Vol. Gos. Univ. Ser. 1 Mat. Fiz., 2013, no. 1, pp. 45–58.
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Original Russian Text © S.A. Korol’kov, 2015, published in Differentsial’nye Uravneniya, 2015, Vol. 51, No. 6, pp. 726–732.
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Korol’kov, S.A. On the solvability of boundary value problems for the stationary Schrödinger equation in unbounded domains on Riemannian manifolds. Diff Equat 51, 738–744 (2015). https://doi.org/10.1134/S001226611506004X
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DOI: https://doi.org/10.1134/S001226611506004X