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Matematicheskie Zametki, 2025, Volume 117, Issue 2, Pages 270–284
DOI: https://doi.org/10.4213/mzm14338 (Mi mzm14338) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Lower bounds for the leading eigenvalue of the Laplacian on a graph

S. A. Karkuzaeva, R. Ch. Kulaevb

a North Ossetian State University after Kosta Levanovich Khetagurov, Vladikavkaz
b Southern Mathematical Institute of the Vladikavkaz Scientific Center of the Russian Academy of Sciences, Vladikavkaz
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DOI: https://doi.org/10.4213/mzm14338
Abstract: The purpose of this paper is to obtain lower bounds for the minimal eigenvalue of the Sturm–Liouville differential operator on a graph. In this way, an analog of the Picone identity for an equation on a network is established. As an application of such an identity, Sturm comparison theorems and properties of differential inequalities for a second-order operator on a graph are obtained.
Keywords: eigenvalue estimation, spectral problem on a graph, Sturm theorems, Picone identity.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-02-2025-1530
This work was financially supported by the Ministry of Science and Higher Education of the Russian Federation (grant no. 075-02-2025-1530).
Received: 06.04.2024
Published: 13.05.2025
English version:
Mathematical Notes, 2025, Volume 117, Issue 2, Pages 287–299
DOI: https://doi.org/10.1134/S0001434625010262
Bibliographic databases:
Document Type: Article
UDC: 517.927
MSC: 34C10, 34B27, 34B24, 34L05
Language: Russian
Citation: S. A. Karkuzaev, R. Ch. Kulaev, “Lower bounds for the leading eigenvalue of the Laplacian on a graph”, Mat. Zametki, 117:2 (2025), 270–284; Math. Notes, 117:2 (2025), 287–299
Citation in format AMSBIB
\Bibitem{KarKul25}
\by S.~A.~Karkuzaev, R.~Ch.~Kulaev
\paper Lower bounds for the leading eigenvalue of the Laplacian on a graph
\jour Mat. Zametki
\yr 2025
\vol 117
\issue 2
\pages 270--284
\mathnet{http://mi.mathnet.ru/mzm14338}
\crossref{https://doi.org/10.4213/mzm14338}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=4908572}
\transl
\jour Math. Notes
\yr 2025
\vol 117
\issue 2
\pages 287--299
\crossref{https://doi.org/10.1134/S0001434625010262}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-105007246271}
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  • https://doi.org/10.4213/mzm14338
  • https://www.mathnet.ru/eng/mzm/v117/i2/p270
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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