Reconstruction of the potential in the Sturm-Liouville equation with spectral boundary conditions
Abstract This study examines the Sturm-Liouville equation, focusing on cases where the spectral parameter is included in the boundary conditions. By employing the Hochstadt-Lieberman theorem and the Weyl function, we demonstrate that when the potential is known for the interval ( 0 , π 2 ) $\left (0...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2025-08-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13660-025-03347-x |
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| Summary: | Abstract This study examines the Sturm-Liouville equation, focusing on cases where the spectral parameter is included in the boundary conditions. By employing the Hochstadt-Lieberman theorem and the Weyl function, we demonstrate that when the potential is known for the interval ( 0 , π 2 ) $\left (0,\frac{\pi}{2}\right )$ , a single spectrum can specify the potential for the whole interval ( 0 , π ) $(0,\pi )$ . Furthermore, utilizing the Gesztesy-Simon theorem alongside the Weyl function technique, we establish that if the potential is known a priori on ( 0 , π / 2 ( 1 − α ) ) $(0,\pi /2(1 - \alpha ))$ as α ∈ ( 0 , 1 ) $\alpha \in (0, 1)$ , some of spectra can uniquely identify the potential across the entire interval ( 0 , π ) $(0, \pi )$ . |
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| ISSN: | 1029-242X |