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Inverse nodal problems for perturbed spherical Schrödinger operators

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Abstract

The inverse nodal problem for perturbed spherical Schrödinger operator defined on (0, 1) is studied. We prove that the potential on the whole interval can be uniquely determined in terms of a twin dense nodal subset known on the interior subinterval \((a,1),a \in (0,1).\)  Especially, when  \(a \in \left( \frac{1}{2},1\right) ,\)  we need additional spectral information, which is associated with the derivatives of eigenfunctions at some known nodal points.

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Funding

This research was supported by the Research Fund Project of Tianjin University of Technology and Education (G. No. KRKC012219); National Natural Science Foundation of China (G. No. 12001153).

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Authors and Affiliations

  1. School of Science, Tianjin University of Technology and Education, Tianjin, 300222, People’s Republic of China

    Yu Liu

  2. School of Mathematics, Tianjin University, Tianjin, 300354, People’s Republic of China

    Guoliang Shi & Jun Yan

  3. School of Science, Hebei University of Technology, Tianjin, 300401, People’s Republic of China

    Jia Zhao

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  1. Yu Liu
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  2. Guoliang Shi
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  4. Jia Zhao
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Contributions

Author 1: Conceptualization; Funding Acquisition; Writing-Original Draft. Author 2: Resources; Supervision; Writing-Review & Editing. Author 3: Conceptualization; Resources; Writing-Review & Editing. Author 4: Funding Acquisition; Writing-Review & Editing.

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Correspondence to Jun Yan.

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Liu, Y., Shi, G., Yan, J. et al. Inverse nodal problems for perturbed spherical Schrödinger operators. Anal.Math.Phys. 13, 73 (2023). https://doi.org/10.1007/s13324-023-00837-3

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  • DOI: https://doi.org/10.1007/s13324-023-00837-3

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