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Matematicheskie Zametki, 2021, Volume 109, Issue 1, Pages 82–100
DOI: https://doi.org/10.4213/mzm12837 (Mi mzm12837) 		 
This article is cited in 8 scientific papers (total in 8 papers)

On Recovering the Sturm–Liouville Differential Operators on Time Scales

M. A. Kuznetsova

Saratov State University
Full-text PDF (588 kB) Citations (8)
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DOI: https://doi.org/10.4213/mzm12837
Abstract: We study Sturm–Liouville differential operators on the time scales consisting of a finite number of isolated points and closed intervals. In the author's previous paper, it was established that such operators are uniquely determined by the spectral characteristics of all classical types. In the present paper, an algorithm for their recovery based on the method of spectral mappings is obtained. We also prove that the eigenvalues of two Sturm–Liouville boundary-value problems on time scales with one common boundary condition alternate.
Keywords: inverse spectral problems, time scales, closed sets, differential operators, Sturm–Liouville equations.
Funding agency Grant number
Russian Science Foundation 19-71-00009
This work was supported by the Russian Science Foundation under grant 19-71-00009.
Received: 16.07.2020
English version:
Mathematical Notes, 2021, Volume 109, Issue 1, Pages 74–88
DOI: https://doi.org/10.1134/S0001434621010090
Bibliographic databases:
Document Type: Article
UDC: 517.984
Language: Russian
Citation: M. A. Kuznetsova, “On Recovering the Sturm–Liouville Differential Operators on Time Scales”, Mat. Zametki, 109:1 (2021), 82–100; Math. Notes, 109:1 (2021), 74–88
Citation in format AMSBIB
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  • https://doi.org/10.4213/mzm12837
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    • This publication is cited in the following 8 articles:
    1. Na Zhang, Ji-Jun Ao, “Eigenvalues of some third-order boundary value problems with eigenparameter-dependent boundary conditions on time scales”, CAC, 2025  crossref
    2. Rauf Amirov, Sevim Durak, “Inverse nodal problems for singular diffusion equation”, Math Methods in App Sciences, 2024  crossref
    3. N. P. Bondarenko, E. E. Chitorkin, “Inverse Sturm–Liouville problem with spectral parameter in the boundary conditions”, Mathematics, 11:5 (2023), 1138  crossref
    4. I. Adalar, “Determination of a differential pencil from interior spectral data on a union of two closed intervals”, Turk. J. Math., 46:1, SI (2022), 377–386  crossref  mathscinet  isi
    5. M. A. Kuznetsova, “Obratnaya zadacha dlya operatora Shturma—Liuvillya s zamorozhennym argumentom na vremennoi shkale”, Materialy Voronezhskoi mezhdunarodnoi vesennei matematicheskoi shkoly «Sovremennye metody teorii kraevykh zadach. Pontryaginskie chteniya–XXXII», Voronezh, 3–9 maya 2021 g.  Chast 1, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 208, VINITI RAN, M., 2022, 49–62  mathnet  crossref
    6. Kaihong Zhao, “Coincidence theory of a nonlinear periodic sturm–liouville system and its applications”, Axioms, 11:12 (2022), 726  crossref
    7. Meng-lei Li, Ji-jun Ao, Hai-yan Zhang, “Dependence of eigenvalues of Sturm-liouville problems on time scales with eigenparameter-dependent boundary conditions”, Open Mathematics, 20:1 (2022), 1215  crossref  mathscinet
    8. Kuznetsova M.A., Buterin S.A., Yurko V.A., “On Inverse Spectral Problems For Sturm-Liouville Differential Operators on Closed Sets”, Lobachevskii J. Math., 42:6, SI (2021), 1201–1209  crossref  mathscinet  zmath  isi
    Citing articles in Google Scholar: Russian citations, English citations
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