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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2024, Number 1, Pages 35–49
DOI: https://doi.org/10.26907/0021-3446-2024-1-35-49
(Mi ivm9948)
 

Asymptotic behavior of solutions of the inhomogeneous Schrödinger equation on noncompact Riemannian manifolds

E. A. Mazepa, D. K. Ryaboshlykova

Volgograd State University, 100 Universitetskiy Ave., Volgograd, 400062 Russia
References:
Abstract: The paper studies the behavior of bounded solutions of the inhomogeneous Schrödinger equation on non-compact Riemannian manifolds under a variation of the right side of the equation. Various problems for homogeneous elliptic equations, in particular the Laplace-Beltrami equation and the stationary Schrödinger equation, have been considered by a number of Russian and foreign authors since the second half of the 20th century. In the first part of this paper, an approach to the formulation of boundary value problems based on the introduction of classes of equivalent functions will be developed. The relationship between the solvability of boundary value problems on an arbitrary non-compact Riemannian manifold with variation of inhomogeneity is also established. In the second part of the work, based on the results of the first part, properties of solutions of the inhomogeneous Schrödinger equation on quasi-model manifolds are investigated, and exact conditions for unique solvability of the Dirichlet problem and some other boundary value problems on these manifolds are found.
Keywords: inhomogeneous Schrödinger equation, boundary value problem, quasi-model Riemannian manifold.
Received: 29.12.2022
Revised: 05.05.2023
Accepted: 29.05.2023
Document Type: Article
UDC: 517.95
Language: Russian
Citation: E. A. Mazepa, D. K. Ryaboshlykova, “Asymptotic behavior of solutions of the inhomogeneous Schrödinger equation on noncompact Riemannian manifolds”, Izv. Vyssh. Uchebn. Zaved. Mat., 2024, no. 1, 35–49
Citation in format AMSBIB
\Bibitem{MazRya24}
\by E.~A.~Mazepa, D.~K.~Ryaboshlykova
\paper Asymptotic behavior of solutions of the inhomogeneous Schr\"odinger equation on noncompact Riemannian manifolds
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2024
\issue 1
\pages 35--49
\mathnet{http://mi.mathnet.ru/ivm9948}
\crossref{https://doi.org/10.26907/0021-3446-2024-1-35-49}
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    Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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