Zubankova K.A., Mazepa E.A., Poluboyarova N.M. On the Asymptotic Behavior of Solutions of the Stationary Schrödinger Equation on Non-Compact Riemannian Manifolds

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https://doi.org/10.15688/mpcm.jvolsu.2023.4.1

Kristina A. Zubankova
Postgraduate Student, Department of Mathematical Analysis and Function Theory,
Volgograd State University
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Prosp. Universitetsky, 100, 400062 Volgograd, Russian Federation

Elena A. Mazepa
Candidate of Sciences (Physics and Mathematics), Associate Professor, Department of Mathematical Analysis and Function Theory,
Volgograd State University
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https://orcid.org/0000-0001-7603-4133
Prosp. Universitetsky, 100, 400062 Volgograd, Russian Federation

Natalya M. Poluboyarova
Candidate of Sciences (Physics and Mathematics), Associate Professor, Department of Computer Sciences and Experimental Mathematics,
Volgograd State University
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https://orcid.org/0000-0002-3973-7574
Prosp. Universitetsky, 100, 400062 Volgograd, Russian Federation

Abstract. We study We study the problem of asymptotic behavior and belonging to given functional class of solutions of the Schrodinger equation on a noncompact Riemannian manifold M without boundary. In the present work we suggest concept of equivalence in the classes of continuous functions on a non-compact Riemannian manifold with respect to certain norms in this spaces. Also we establish the interrelation between problems of existence of solutions of the Schrodinger equation on M and off some compact in a given class of equivalent functions

Key words: first boundary value problem, loaded equation, heat equation, difference scheme, a priori estimate, stability and convergence.

On the Existence and Uniqueness of a Positive Solution to a Boundary Value Problem for a Nonlinear Ordinary Differential Fourth Order Equation by Zubankova K.A., Mazepa E.A., Poluboyarova N.M. is licensed under a Creative Commons Attribution 4.0 International License.

Citation in English: Mathematical Physics and Computer Simulation. Vol. 26 No. 4 2023, pp. 18-30

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