Asymptotics of the eigenvalues of a boundary value problem for the operator Schrödinger equation with boundary conditions nonlinearly dependent on the spectral parameter
On the space H1 = L2(H, [0, 1]), where H is a separable Hilbert space, we study the asymptotic behavior of the eigenvalues of a boundary value problem for the operator Schrödinger equation for the case when one, and the same, spectral parameter participates linearly in the equation and quadraticall...
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| Format: | Article |
| Language: | English |
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Samara State Technical University
2021-12-01
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| Series: | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
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| Online Access: | https://journals.eco-vector.com/1991-8615/article/viewFile/89723/pdf |
| _version_ | 1818025027679813632 |
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| author | Ilyas F. Hashimoglu |
| author_facet | Ilyas F. Hashimoglu |
| author_sort | Ilyas F. Hashimoglu |
| collection | DOAJ |
| description | On the space H1 = L2(H, [0, 1]), where H is a separable Hilbert space, we study the asymptotic behavior of the eigenvalues of a boundary value problem for the operator Schrödinger equation for the case when one, and the same, spectral parameter participates linearly in the equation and quadratically in the boundary condition. Asymptotic formulae are obtained for the eigenvalues of the considered boundary value problem. |
| first_indexed | 2024-12-10T04:09:35Z |
| format | Article |
| id | doaj.art-93a67775c74c480a979178a280ff1dff |
| institution | Directory Open Access Journal |
| issn | 1991-8615 2310-7081 |
| language | English |
| last_indexed | 2024-12-10T04:09:35Z |
| publishDate | 2021-12-01 |
| publisher | Samara State Technical University |
| record_format | Article |
| series | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
| spelling | doaj.art-93a67775c74c480a979178a280ff1dff2022-12-22T02:02:46ZengSamara State Technical UniversityVestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki1991-86152310-70812021-12-0125460761510.14498/vsgtu189477803Asymptotics of the eigenvalues of a boundary value problem for the operator Schrödinger equation with boundary conditions nonlinearly dependent on the spectral parameterIlyas F. Hashimoglu0https://orcid.org/0000-0002-1690-2186Karabük UniversityOn the space H1 = L2(H, [0, 1]), where H is a separable Hilbert space, we study the asymptotic behavior of the eigenvalues of a boundary value problem for the operator Schrödinger equation for the case when one, and the same, spectral parameter participates linearly in the equation and quadratically in the boundary condition. Asymptotic formulae are obtained for the eigenvalues of the considered boundary value problem.https://journals.eco-vector.com/1991-8615/article/viewFile/89723/pdfoperator differential equationsspectrumeigenvalueasymptotic formulahilbert space |
| spellingShingle | Ilyas F. Hashimoglu Asymptotics of the eigenvalues of a boundary value problem for the operator Schrödinger equation with boundary conditions nonlinearly dependent on the spectral parameter Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki operator differential equations spectrum eigenvalue asymptotic formula hilbert space |
| title | Asymptotics of the eigenvalues of a boundary value problem for the operator Schrödinger equation with boundary conditions nonlinearly dependent on the spectral parameter |
| title_full | Asymptotics of the eigenvalues of a boundary value problem for the operator Schrödinger equation with boundary conditions nonlinearly dependent on the spectral parameter |
| title_fullStr | Asymptotics of the eigenvalues of a boundary value problem for the operator Schrödinger equation with boundary conditions nonlinearly dependent on the spectral parameter |
| title_full_unstemmed | Asymptotics of the eigenvalues of a boundary value problem for the operator Schrödinger equation with boundary conditions nonlinearly dependent on the spectral parameter |
| title_short | Asymptotics of the eigenvalues of a boundary value problem for the operator Schrödinger equation with boundary conditions nonlinearly dependent on the spectral parameter |
| title_sort | asymptotics of the eigenvalues of a boundary value problem for the operator schrodinger equation with boundary conditions nonlinearly dependent on the spectral parameter |
| topic | operator differential equations spectrum eigenvalue asymptotic formula hilbert space |
| url | https://journals.eco-vector.com/1991-8615/article/viewFile/89723/pdf |
| work_keys_str_mv | AT ilyasfhashimoglu asymptoticsoftheeigenvaluesofaboundaryvalueproblemfortheoperatorschrodingerequationwithboundaryconditionsnonlinearlydependentonthespectralparameter |