Inverse spectral problem for differential pencils with a frozen argument
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916206086193152 |
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| author | Hu, Yi-teng Sat, Murat |
| author_facet | Hu, Yi-teng Sat, Murat |
| contents | This paper deals with differential pencils possessing a term depending on the unknown function with a fixed argument. We deduce the so called main equation together with its fine structure for the spectral problem. Then, according to the boundary conditions and the position of argument, we describe two cases: degenerate and non-degenerate. For these two cases, the uniqueness of inverse spectral problem are studied and a constructive procedure for reconstructing the potentials along with necessary and sufficient conditions of its solvability are obtained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_02529 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Inverse spectral problem for differential pencils with a frozen argument Hu, Yi-teng Sat, Murat Classical Analysis and ODEs Spectral Theory This paper deals with differential pencils possessing a term depending on the unknown function with a fixed argument. We deduce the so called main equation together with its fine structure for the spectral problem. Then, according to the boundary conditions and the position of argument, we describe two cases: degenerate and non-degenerate. For these two cases, the uniqueness of inverse spectral problem are studied and a constructive procedure for reconstructing the potentials along with necessary and sufficient conditions of its solvability are obtained. |
| title | Inverse spectral problem for differential pencils with a frozen argument |
| topic | Classical Analysis and ODEs Spectral Theory |
| url | https://arxiv.org/abs/2305.02529 |