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A Partial Inverse Problem for the Differential Pencil on a Star-Shaped Graph

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Abstract

The quadratic pencil of Sturm–Liouville operators on a star-shaped graph is investigated. We suppose that the coefficients of the pencil are known for all the edges of the graph except one, and study the partial inverse problem, which consists in recovering the remaining coefficients from the part of the spectrum. We prove the uniqueness theorem and provide a constructive algorithm for the solution of the partial inverse problem.

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Authors and Affiliations

  1. Department of Applied Mathematics, Samara National Research University, Moskovskoye Shosse 34, Samara, Russia, 443086

    Natalia P. Bondarenko

  2. Department of Mechanics and Mathematics, Saratov State University, Astrakhanskaya 83, Saratov, Russia, 410012

    Natalia P. Bondarenko

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  1. Natalia P. Bondarenko
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Correspondence to Natalia P. Bondarenko.

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Bondarenko, N.P. A Partial Inverse Problem for the Differential Pencil on a Star-Shaped Graph. Results Math 72, 1933–1942 (2017). https://doi.org/10.1007/s00025-017-0683-7

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  • DOI: https://doi.org/10.1007/s00025-017-0683-7

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