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The Partial Inverse Spectral and Nodal Problems for Sturm–Liouville Operators on a Star-Shaped Graph

Author

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  • Xian-Biao Wei

    (Department of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China)

  • Yan-Hsiou Cheng

    (Department of Mathematics and Information Education, National Taipei University of Education, Taipei City 106, Taiwan)

  • Yu-Ping Wang

    (Department of Applied Mathematics, Nanjing Forestry University, Nanjing 210037, China)

Abstract

We firstly prove the Horváth-type theorem for Sturm–Liouville operators on a star-shaped graph and then solve a new partial inverse nodal problem for this operator. We give some algorithms to recover this operator from a dense nodal subset and prove uniqueness theorems from paired-dense nodal subsets in interior subintervals having a central vertex. In particular, we obtain some uniqueness theorems by replacing the information of nodal data on some fixed edge with part of the eigenvalues under some conditions.

Suggested Citation

  • Xian-Biao Wei & Yan-Hsiou Cheng & Yu-Ping Wang, 2022. "The Partial Inverse Spectral and Nodal Problems for Sturm–Liouville Operators on a Star-Shaped Graph," Mathematics, MDPI, vol. 10(21), pages 1-21, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:21:p:3971-:d:953382
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    References listed on IDEAS

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    1. Barilla, David & Bohner, Martin & Heidarkhani, Shapour & Moradi, Shahin, 2021. "Existence results for dynamic Sturm–Liouville boundary value problems via variational methods," Applied Mathematics and Computation, Elsevier, vol. 409(C).
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