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Matematicheskie Zametki, 2014, Volume 96, Issue 6, Pages 885–895
DOI: https://doi.org/10.4213/mzm10268 (Mi mzm10268) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Estimate of the First Eigenvalue of the Laplacian on a Graph

A. T. Diaba, P. A. Kuleshovb, O. M. Penkinb

a Ain Shams University
b Voronezh State University
Full-text PDF (495 kB) Citations (7)
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DOI: https://doi.org/10.4213/mzm10268
Abstract: The eigenvalue problem for the Laplacian with Dirichlet boundary conditions on a graph is considered. The main result is an estimate of the first (minimal) eigenvalue. The proof is based on the Schwartz symmetrization of a function on a graph and on its properties.
Keywords: eigenvalue problem, Schwartz symmetrization, Laplacian on a graph.
Received: 26.02.2013
Revised: 18.05.2013
English version:
Mathematical Notes, 2014, Volume 96, Issue 6, Pages 948–956
DOI: https://doi.org/10.1134/S0001434614110327
Bibliographic databases:
Document Type: Article
UDC: 517.923
Language: Russian
Citation: A. T. Diab, P. A. Kuleshov, O. M. Penkin, “Estimate of the First Eigenvalue of the Laplacian on a Graph”, Mat. Zametki, 96:6 (2014), 885–895; Math. Notes, 96:6 (2014), 948–956
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/mzm/v96/i6/p885
    • This publication is cited in the following 7 articles:
    1. S. A. Karkuzaev, R. Ch. Kulaev, “Nizhnie otsenki veduschego sobstvennogo znacheniya laplasiana na grafe”, Matem. zametki, 117:2 (2025), 270–284  mathnet  crossref
    2. 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  crossref
    3. 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  crossref
    4. 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  crossref
    5. 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  mathnet  crossref  mathscinet
    6. 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  mathnet  crossref  crossref  isi
    7. A. A. Vladimirov, “Remarks on Minorants of Laplacians on a Geometric Graph”, Math. Notes, 98:3 (2015), 519–521  mathnet  crossref  crossref  mathscinet  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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