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Matematicheskie Zametki, 2016, Volume 99, Issue 4, Pages 489–501
DOI: https://doi.org/10.4213/mzm10461 (Mi mzm10461) 		 
This article is cited in 7 scientific papers (total in 7 papers)

On the Multiplicity of Eigenvalues of the Sturm–Liouville Problem on Graphs

A. T. Diaba, B. K. Kaldybekovab, O. M. Penkincb

a Ain Shams University
b Kazakh-British Technical University
c Voronezh State University
Full-text PDF (511 kB) Citations (7)
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DOI: https://doi.org/10.4213/mzm10461
Abstract: Bounds for the multiplicity of the eigenvalues of the Sturm–Liouville problem on a graph, which are valid for a wide class of consistency (transmission) conditions at the vertices of the graph, are given. The multiplicities are estimated using the topological characteristics of the graph. In the framework of the notions that we use, the bounds turn out to be exact.
Keywords: geometric graph, ordinary differential equation on a graph, Sturm–Liouville problem on a graph, transmission conditions, multiplicity of eigenvalues.
Funding agency Grant number
Ministry of Education and Science of the Republic of Kazakhstan 0115РК00643
0115РК02687
This work was supported by the Ministry of Education and Science of the Republic of Kazakhstan (projects 0115RK00643 and 0115RK02687).
Received: 23.03.2014
Revised: 09.08.2015
English version:
Mathematical Notes, 2016, Volume 99, Issue 4, Pages 492–502
DOI: https://doi.org/10.1134/S0001434616030226
Bibliographic databases:
Document Type: Article
UDC: 517.927
Language: Russian
Citation: A. T. Diab, B. K. Kaldybekova, O. M. Penkin, “On the Multiplicity of Eigenvalues of the Sturm–Liouville Problem on Graphs”, Mat. Zametki, 99:4 (2016), 489–501; Math. Notes, 99:4 (2016), 492–502
Citation in format AMSBIB
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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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