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

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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 11 scientific papers (total in 11 papers)

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

A. T. Diab^a, B. K. Kaldybekova^b, O. M. Penkin^cb

^a Ain Shams University
^b Kazakh-British Technical University
^c Voronezh State University

Full-text PDF (511 kB) Citations (11)

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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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https://doi.org/10.4213/mzm10461

https://www.mathnet.ru/eng/mzm/v99/i4/p489

This publication is cited in the following 11 articles:

S. A. Karkuzaev, R. Ch. Kulaev, “Nizhnie otsenki veduschego sobstvennogo znacheniya laplasiana na grafe”, Matem. zametki, 117:2 (2025), 270–284
M. B. Zvereva, “A Model of String System Deformations on a Star Graph with Nonlinear Condition at the Node”, J Math Sci, 283:1 (2024), 76
A. A. Urtaeva, “Upper bounds for the eigenvalue multiplicities of a fourth-order differential operator on a graph”, J. Appl. Industr. Math., 18:2 (2024), 352–360
M. B. Zvereva, M. I. Kamenskii, “Problem on string system vibrations on star-shaped graph with nonlinear condition at node”, Ufa Math. J., 16:1 (2024), 34–52
R. Ch Kulaev, S. A Karkuzaev, “BOTTOM ESTIMATES FOR THE MINIMAL EIGENVALUE OF THE BI-LAPLACIAN ON A GRAPH”, Differencialʹnye uravneniâ, 60:8 (2024), 1034
R. Ch. Kulaev, S. A. Karkuzaev, “Lower Bounds for the Minimum Eigenvalue of the bi-Laplacian on a Graph”, Diff Equat, 60:8 (2024), 1014
M. Sh. Burlutskaya, M. B. Zvereva, M. I. Kamenskii, “Boundary Value Problem on a Geometric Star-Graph with a Nonlinear Condition at a Node”, Math. Notes, 114:2 (2023), 275–279
M. B. Zvereva, “Model deformatsii sistemy stiltesovskikh strun s nelineinym usloviem”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 32:4 (2022), 528–545
M. B. Zvereva, “Model deformatsii strunnoi sistemy na grafe-zvezde s nelineinym usloviem v uzle”, Differentsialnye i funktsionalno-differentsialnye uravneniya, SMFN, 68, no. 4, Rossiiskii universitet druzhby narodov, M., 2022, 635–652
R. Ch. Kulaev, A. A. Urtaeva, “On the Multiplicity of Eigenvalues of a Fourth-Order Differential Operator on a Graph”, Diff Equat, 58:7 (2022), 869
M. Sh. Burlutskaya, “Some properties of functional-differential operators with involution $\nu(x)=1-x$ and their applications”, Russian Math. (Iz. VUZ), 65:5 (2021), 69–76

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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