Borg-type theorem for a class of fourth-order differential operators
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916516699570176 |
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| author | Guan, Ai-Wei Yang, Chuan-Fu Bondarenko, Natalia P. |
| author_facet | Guan, Ai-Wei Yang, Chuan-Fu Bondarenko, Natalia P. |
| contents | In this paper, we study an inverse spectral problem for the fourth-order differential equation $y^{(4)} - (p y')' + q y = λy$ with real-valued coefficients $p$ and $q$ of $L^2(0,1)$. We prove that, for near-constant coefficients, the two spectra corresponding to the Dirichlet and the Dirichlet-Neumann boundary conditions uniquely determine either $p$ or $q$. The result extends the Borg theorem of the second-order case to the fourth-order case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_07413 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Borg-type theorem for a class of fourth-order differential operators Guan, Ai-Wei Yang, Chuan-Fu Bondarenko, Natalia P. Spectral Theory In this paper, we study an inverse spectral problem for the fourth-order differential equation $y^{(4)} - (p y')' + q y = λy$ with real-valued coefficients $p$ and $q$ of $L^2(0,1)$. We prove that, for near-constant coefficients, the two spectra corresponding to the Dirichlet and the Dirichlet-Neumann boundary conditions uniquely determine either $p$ or $q$. The result extends the Borg theorem of the second-order case to the fourth-order case. |
| title | Borg-type theorem for a class of fourth-order differential operators |
| topic | Spectral Theory |
| url | https://arxiv.org/abs/2412.07413 |