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On Recovering Sturm–Liouville-Type Operators with Global Delay on Graphs from Two Spectra

Author

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  • Sergey Buterin

    (Department of Mathematics, Saratov State University, 410012 Saratov, Russia)

Abstract

We suggest a new formulation of the inverse spectral problem for second-order functional-differential operators on star-shaped graphs with global delay. The latter means that the delay, which is measured in the direction of a specific boundary vertex, called the root, propagates through the internal vertex to other edges. Now, we intend to recover the potentials from the spectra of two boundary value problems on the graph with a common set of boundary conditions at all boundary vertices except the root. For simplicity, we focus on star graphs with equal edges when the delay parameter is not less than their length. Under the assumption that the common boundary conditions are of the Robin type and they are known and pairwise linearly independent, the uniqueness theorem is proven and a constructive procedure for solving the proposed inverse problem is obtained.

Suggested Citation

  • Sergey Buterin, 2023. "On Recovering Sturm–Liouville-Type Operators with Global Delay on Graphs from Two Spectra," Mathematics, MDPI, vol. 11(12), pages 1-12, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:12:p:2688-:d:1170314
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    References listed on IDEAS

    as
    1. Buterin, S.A. & Malyugina, M.A. & Shieh, C.-T., 2021. "An inverse spectral problem for second-order functional-differential pencils with two delays," Applied Mathematics and Computation, Elsevier, vol. 411(C).
    2. Hu, Yi-teng & Bondarenko, Natalia Pavlovna & Shieh, Chung-Tsun & Yang, Chuan-fu, 2019. "Traces and inverse nodal problems for Dirac-type integro-differential operators on a graph," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
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    1. Buterin, S.A. & Malyugina, M.A. & Shieh, C.-T., 2021. "An inverse spectral problem for second-order functional-differential pencils with two delays," Applied Mathematics and Computation, Elsevier, vol. 411(C).
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