Gulmanova E.A., Klyachin A.A., Mazepa Е.А. Generalized solutions of the Dirichlet problem for the stationary Schrodinger equation on Riemannian manifolds

Gulmanova Elena Ataevna
 
Postgraduate student, Assistant, Department of Mathematical Analysis and Function Theory, Volgograd State University
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Prospekt Universitetskij, 100, 400062 Volgograd, Russian Federation
 
Klyachin Alexey Alexandrovich
 
Doctor of Physics and Mathematics, Head of Department of Mathematical Analysis and Function Theory, Volgograd State University
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Prospekt Universitetskij, 100, 400062 Volgograd, Russian Federation
 
Mazepa Elena Alekseevna
 
Candidate of Physics and Mathematics, Associate Professor, Department of Fundamental Information Science and Optimal Control, Volgograd State University
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Prospekt Universitetskij, 100, 400062 Volgograd, Russian Federation
 
Abstract. We study questions of existence of generalized solutions of the Dirichlet problem for the basic models of elliptical equations: the Laplace equation ∆u = 0, and the stationary Schrodinger equations Lu ≡ ∆u−c(x)u = 0, where c(x) is a smooth non-negative function on a non-compact Riemannian manifolds M without boundary.
In this arcticle the concept of generalized solutions of the problem is specified and the investigation of guestions of existence Dirichlet problem is affoded to investigation this
generalized solution.
 
Key words: the stationary Schrodinger equation, the deneralized solution of Dirichlet problems, Riemannian manifolds.

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Generalized solutions of the Dirichlet problem for the stationary Schrodinger equation on Riemannian manifolds by Gulmanova E.A., Klyachin A.A., Mazepa Е.А. is licensed under a Creative Commons Attribution 4.0 International License.

Citation in English: Science Journal of Volgograd State University. Mathematics. Physics. Issue 13 2010 pp. 36-40
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