A Class of Singular Sturm–Liouville Problems with Discontinuity and an Eigenparameter-Dependent Boundary Condition
In this paper, we study a singular Sturm–Liouville problem with an eigenparameter-dependent boundary condition and transmission conditions at two interior points. Using an operator-theoretical formulation, we transfer the problem to an operator in an appropriate Hilbert space. It is proved that the...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-11-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/23/4430 |
| _version_ | 1827642985512173568 |
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| author | Jinming Cai Zhaowen Zheng Kun Li |
| author_facet | Jinming Cai Zhaowen Zheng Kun Li |
| author_sort | Jinming Cai |
| collection | DOAJ |
| description | In this paper, we study a singular Sturm–Liouville problem with an eigenparameter-dependent boundary condition and transmission conditions at two interior points. Using an operator-theoretical formulation, we transfer the problem to an operator in an appropriate Hilbert space. It is proved that the operator is self-adjoint. We also give the asymptotic formulas of the eigenvalues of the problem. Moreover, Green’s function is also discussed. |
| first_indexed | 2024-03-09T17:40:28Z |
| format | Article |
| id | doaj.art-30bbcc50ce6f4f58960b0cf34d8b1518 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T17:40:28Z |
| publishDate | 2022-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-30bbcc50ce6f4f58960b0cf34d8b15182023-11-24T11:33:24ZengMDPI AGMathematics2227-73902022-11-011023443010.3390/math10234430A Class of Singular Sturm–Liouville Problems with Discontinuity and an Eigenparameter-Dependent Boundary ConditionJinming Cai0Zhaowen Zheng1Kun Li2School of Mathematical Sciences, Qufu Normal University, Qufu 273165, ChinaSchool of Mathematical Sciences, Qufu Normal University, Qufu 273165, ChinaSchool of Mathematical Sciences, Qufu Normal University, Qufu 273165, ChinaIn this paper, we study a singular Sturm–Liouville problem with an eigenparameter-dependent boundary condition and transmission conditions at two interior points. Using an operator-theoretical formulation, we transfer the problem to an operator in an appropriate Hilbert space. It is proved that the operator is self-adjoint. We also give the asymptotic formulas of the eigenvalues of the problem. Moreover, Green’s function is also discussed.https://www.mdpi.com/2227-7390/10/23/4430singular Sturm–Liouville problemtransmission conditioneigenparameter-dependent boundary conditionasymptotic formula of an eigenvalueGreen’s function |
| spellingShingle | Jinming Cai Zhaowen Zheng Kun Li A Class of Singular Sturm–Liouville Problems with Discontinuity and an Eigenparameter-Dependent Boundary Condition Mathematics singular Sturm–Liouville problem transmission condition eigenparameter-dependent boundary condition asymptotic formula of an eigenvalue Green’s function |
| title | A Class of Singular Sturm–Liouville Problems with Discontinuity and an Eigenparameter-Dependent Boundary Condition |
| title_full | A Class of Singular Sturm–Liouville Problems with Discontinuity and an Eigenparameter-Dependent Boundary Condition |
| title_fullStr | A Class of Singular Sturm–Liouville Problems with Discontinuity and an Eigenparameter-Dependent Boundary Condition |
| title_full_unstemmed | A Class of Singular Sturm–Liouville Problems with Discontinuity and an Eigenparameter-Dependent Boundary Condition |
| title_short | A Class of Singular Sturm–Liouville Problems with Discontinuity and an Eigenparameter-Dependent Boundary Condition |
| title_sort | class of singular sturm liouville problems with discontinuity and an eigenparameter dependent boundary condition |
| topic | singular Sturm–Liouville problem transmission condition eigenparameter-dependent boundary condition asymptotic formula of an eigenvalue Green’s function |
| url | https://www.mdpi.com/2227-7390/10/23/4430 |
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