On the solvability of boundary value problems for the stationary Schrödinger equation in unbounded domains on Riemannian manifolds

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...

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Bibliographic Details
Published in:Differential equations 2015-06, Vol.51 (6), p.738-744
Main Author: Korol’kov, S. A.
Format: Article
Language:English
Subjects:
Boundaries
Boundary value problems
Difference and Functional Equations
Differential equations
Dirichlet problem
Equivalence
Euclidean space
Manifolds
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Schrodinger equation
Schroedinger equation
Studies
Theorems
Topological manifolds
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Summary: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.
ISSN:0012-2661
1608-3083
DOI:10.1134/S001226611506004X