Sturm-Liouville problems with nonlinear dependence on the spectral parameter in the boundary conditions
Abstract In this study, asymptotic estimates of the eigenvalues and eigenfunctions are obtained for the Sturm-Liouville problem on a finite interval with boundary conditions depending polynomially on the spectral parameter. Besides, the derivations of the eigenfunctions are derived. Using the eigenf...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-08-01
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| Series: | Boundary Value Problems |
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| Online Access: | https://doi.org/10.1186/s13661-025-02086-8 |
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| _version_ | 1849226057985556480 |
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| author | Ayşe Kabataş |
| author_facet | Ayşe Kabataş |
| author_sort | Ayşe Kabataş |
| collection | DOAJ |
| description | Abstract In this study, asymptotic estimates of the eigenvalues and eigenfunctions are obtained for the Sturm-Liouville problem on a finite interval with boundary conditions depending polynomially on the spectral parameter. Besides, the derivations of the eigenfunctions are derived. Using the eigenfunctions and their derivations, Green’s function of the related problem is calculated. The error bounds in the obtained results are sharper than the existing results in the literature. |
| format | Article |
| id | doaj-art-47e2ad5ac73846be9430caee1334d2c5 |
| institution | Kabale University |
| issn | 1687-2770 |
| language | English |
| publishDate | 2025-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj-art-47e2ad5ac73846be9430caee1334d2c52025-08-24T11:41:22ZengSpringerOpenBoundary Value Problems1687-27702025-08-012025111610.1186/s13661-025-02086-8Sturm-Liouville problems with nonlinear dependence on the spectral parameter in the boundary conditionsAyşe Kabataş0Department of Mathematics, Faculty of Sciences, Karadeniz Technical UniversityAbstract In this study, asymptotic estimates of the eigenvalues and eigenfunctions are obtained for the Sturm-Liouville problem on a finite interval with boundary conditions depending polynomially on the spectral parameter. Besides, the derivations of the eigenfunctions are derived. Using the eigenfunctions and their derivations, Green’s function of the related problem is calculated. The error bounds in the obtained results are sharper than the existing results in the literature.https://doi.org/10.1186/s13661-025-02086-8Sturm-Liouville problemsAsymptotic formulaeEigenvaluesEigenfunctionsGreen’s function |
| spellingShingle | Ayşe Kabataş Sturm-Liouville problems with nonlinear dependence on the spectral parameter in the boundary conditions Boundary Value Problems Sturm-Liouville problems Asymptotic formulae Eigenvalues Eigenfunctions Green’s function |
| title | Sturm-Liouville problems with nonlinear dependence on the spectral parameter in the boundary conditions |
| title_full | Sturm-Liouville problems with nonlinear dependence on the spectral parameter in the boundary conditions |
| title_fullStr | Sturm-Liouville problems with nonlinear dependence on the spectral parameter in the boundary conditions |
| title_full_unstemmed | Sturm-Liouville problems with nonlinear dependence on the spectral parameter in the boundary conditions |
| title_short | Sturm-Liouville problems with nonlinear dependence on the spectral parameter in the boundary conditions |
| title_sort | sturm liouville problems with nonlinear dependence on the spectral parameter in the boundary conditions |
| topic | Sturm-Liouville problems Asymptotic formulae Eigenvalues Eigenfunctions Green’s function |
| url | https://doi.org/10.1186/s13661-025-02086-8 |
| work_keys_str_mv | AT aysekabatas sturmliouvilleproblemswithnonlineardependenceonthespectralparameterintheboundaryconditions |