IJPAM: Volume 97, No. 2 (2014)

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

Elena Korolkova$^1$, Sergei Korolkov$^2$, Andrey Svetlov$^3$
$^{1,2}$Mathematics and IT Department
Volgograd State University
Pr. Universitetskiy, 100, Volgograd, 400062, RUSSIA


Abstract. 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.

Received: July 6, 2014

AMS Subject Classification: 58J32

Key Words and Phrases: boundary value problem, $L$-harmonic function, Riemannian manifold, Dirichlet problem, model manifold

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DOI: 10.12732/ijpam.v97i2.12 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 97
Issue: 2
Pages: 231 - 240


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