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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Main Author: Ayşe Kabataş
Format: Article
Language:English
Published: SpringerOpen 2025-08-01
Series:Boundary Value Problems
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Online Access:https://doi.org/10.1186/s13661-025-02086-8
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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.
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institution Kabale University
issn 1687-2770
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publisher SpringerOpen
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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