Properties of Eigenvalues and Generalized Eigenfunctions for Sturm–Liouville Problem with Eigenparameter-Dependent Boundary Conditions
This paper investigates the eigenvalues and generalized eigenfunctions of a Sturm–Liouville problem in which the eigenparameter appears in the boundary conditions. By employing operator pencil theory in a Hilbert space, combined with an appropriate integral transformation, we prove that the system o...
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| Vydáno v: | Mediterranean journal of mathematics Ročník 22; číslo 8; s. 222 |
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| Jazyk: | angličtina |
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Springer Nature B.V
01.12.2025
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| Abstract | This paper investigates the eigenvalues and generalized eigenfunctions of a Sturm–Liouville problem in which the eigenparameter appears in the boundary conditions. By employing operator pencil theory in a Hilbert space, combined with an appropriate integral transformation, we prove that the system of generalized eigenfunctions forms a Riesz basis. Furthermore, we demonstrate that the spectrum consists of a countably infinite set of real, discrete eigenvalues accumulating at infinity and provide a lower bound estimation for the eigenvalues. |
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| AbstractList | This paper investigates the eigenvalues and generalized eigenfunctions of a Sturm–Liouville problem in which the eigenparameter appears in the boundary conditions. By employing operator pencil theory in a Hilbert space, combined with an appropriate integral transformation, we prove that the system of generalized eigenfunctions forms a Riesz basis. Furthermore, we demonstrate that the spectrum consists of a countably infinite set of real, discrete eigenvalues accumulating at infinity and provide a lower bound estimation for the eigenvalues. |
| ArticleNumber | 222 |
| Author | Li, Zhiyu Zheng, Zhaowen Zhang, Yinghan |
| Author_xml | – sequence: 1 givenname: Zhiyu surname: Li fullname: Li, Zhiyu – sequence: 2 givenname: Zhaowen surname: Zheng fullname: Zheng, Zhaowen – sequence: 3 givenname: Yinghan surname: Zhang fullname: Zhang, Yinghan |
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| Cites_doi | 10.1017/S030821050002521X 10.1016/j.jde.2023.01.047 10.1016/j.jmaa.2006.05.058 10.1016/S0377-0427(02)00579-4 10.1007/BF01083136 10.1007/s00033-025-02583-x 10.1070/SM2000v191n03ABEH000461 10.1007/978-1-4757-4317-3 10.1007/s13324-018-0242-8 10.1063/1.4979615 10.1007/978-3-0348-9152-3 10.1007/s13324-019-00348-0 10.1063/1.5048692 10.1016/j.jde.2005.05.002 10.1017/S0013091501000773 10.1007/BF01084754 10.1090/qam/1637056 10.1007/BF01177870 |
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| SubjectTerms | Boundary conditions Eigenvalues Eigenvectors Hilbert space Integral transforms Lower bounds Operators (mathematics) Ordinary differential equations Sturm-Liouville theory |
| Title | Properties of Eigenvalues and Generalized Eigenfunctions for Sturm–Liouville Problem with Eigenparameter-Dependent Boundary Conditions |
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