On Recovering Sturm--Liouville-Type Operator with Delay and Jump Conditions
In this manuscript, the second order differential operators with constant delay and transmission boundary conditions are studied. The asymptotic forms of the characteristic functions and eigenvalues of the operators are obtained. Therefore, an inverse spectral problem of recovering the operators us...
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| Language: | English |
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University of Maragheh
2024-10-01
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| Series: | Sahand Communications in Mathematical Analysis |
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| Online Access: | https://scma.maragheh.ac.ir/article_716267_4c0219bd3b51b810df10717a777c2b2f.pdf |
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| author | Mohammad Shahriari Vladimir Vladicic |
| author_facet | Mohammad Shahriari Vladimir Vladicic |
| author_sort | Mohammad Shahriari |
| collection | DOAJ |
| description | In this manuscript, the second order differential operators with constant delay and transmission boundary conditions are studied. The asymptotic forms of the characteristic functions and eigenvalues of the operators are obtained. Therefore, an inverse spectral problem of recovering the operators using the spectra of two different Dirichlet-Dirichlet and Dirichlet-Neumann problems, is investigated. For this purpose, to prove the uniqueness of the potential, the integral equations of the potential function are formulated and then utilized. Indirectly, by calculating the coefficients of Fourier series, the potential function is reconstructed. |
| format | Article |
| id | doaj-art-9d26fde079be4a5f8a09a345af7e909e |
| institution | Kabale University |
| issn | 2322-5807 2423-3900 |
| language | English |
| publishDate | 2024-10-01 |
| publisher | University of Maragheh |
| record_format | Article |
| series | Sahand Communications in Mathematical Analysis |
| spelling | doaj-art-9d26fde079be4a5f8a09a345af7e909e2025-02-11T05:27:49ZengUniversity of MaraghehSahand Communications in Mathematical Analysis2322-58072423-39002024-10-0121424125910.22130/scma.2024.2028336.1720716267On Recovering Sturm--Liouville-Type Operator with Delay and Jump ConditionsMohammad Shahriari0Vladimir Vladicic1Department of Mathematics, Faculty of Science, University of Maragheh, P.O. Box 55136-553, Maragheh, Iran.Department of Mathematics, University of East Sarajevo, 71123, East Sarajevo, Bosnia and Herzegovina.In this manuscript, the second order differential operators with constant delay and transmission boundary conditions are studied. The asymptotic forms of the characteristic functions and eigenvalues of the operators are obtained. Therefore, an inverse spectral problem of recovering the operators using the spectra of two different Dirichlet-Dirichlet and Dirichlet-Neumann problems, is investigated. For this purpose, to prove the uniqueness of the potential, the integral equations of the potential function are formulated and then utilized. Indirectly, by calculating the coefficients of Fourier series, the potential function is reconstructed.https://scma.maragheh.ac.ir/article_716267_4c0219bd3b51b810df10717a777c2b2f.pdfdifferential operators with delayinverse spectral problemsdiscontinuity boundary conditionsintegral equations |
| spellingShingle | Mohammad Shahriari Vladimir Vladicic On Recovering Sturm--Liouville-Type Operator with Delay and Jump Conditions Sahand Communications in Mathematical Analysis differential operators with delay inverse spectral problems discontinuity boundary conditions integral equations |
| title | On Recovering Sturm--Liouville-Type Operator with Delay and Jump Conditions |
| title_full | On Recovering Sturm--Liouville-Type Operator with Delay and Jump Conditions |
| title_fullStr | On Recovering Sturm--Liouville-Type Operator with Delay and Jump Conditions |
| title_full_unstemmed | On Recovering Sturm--Liouville-Type Operator with Delay and Jump Conditions |
| title_short | On Recovering Sturm--Liouville-Type Operator with Delay and Jump Conditions |
| title_sort | on recovering sturm liouville type operator with delay and jump conditions |
| topic | differential operators with delay inverse spectral problems discontinuity boundary conditions integral equations |
| url | https://scma.maragheh.ac.ir/article_716267_4c0219bd3b51b810df10717a777c2b2f.pdf |
| work_keys_str_mv | AT mohammadshahriari onrecoveringsturmliouvilletypeoperatorwithdelayandjumpconditions AT vladimirvladicic onrecoveringsturmliouvilletypeoperatorwithdelayandjumpconditions |