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Matematicheskie Zametki, 2013, Volume 93, Issue 4, Pages 537–548
DOI: https://doi.org/10.4213/mzm9023 (Mi mzm9023) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Asymptotics of Eigenvalues of the Two-Dimensional Dirichlet Boundary-Value Problem for the Lamé Operator in a Domain with a Small Hole

D. B. Davletov

Bashkir State Pedagogical University
Full-text PDF (497 kB) Citations (4)
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DOI: https://doi.org/10.4213/mzm9023
Abstract: The Dirichlet boundary-value problem for the eigenvalues of the Lamé operator in a two-dimensional bounded domain with a small hole is studied. The asymptotics of the eigenvalue of this boundary-value problem is constructed and justified up to the power of the parameter defining the diameter of the hole.
Keywords: Dirichlet boundary-value problem, Lamé operator, Fredholm alternative, holomorphic function, asymptotics of eigenvalues, Bessel function.
Received: 10.11.2010
Revised: 09.12.2011
English version:
Mathematical Notes, 2013, Volume 93, Issue 4, Pages 545–555
DOI: https://doi.org/10.1134/S000143461303022X
Bibliographic databases:
Document Type: Article
UDC: 517.956
Language: Russian
Citation: D. B. Davletov, “Asymptotics of Eigenvalues of the Two-Dimensional Dirichlet Boundary-Value Problem for the Lamé Operator in a Domain with a Small Hole”, Mat. Zametki, 93:4 (2013), 537–548; Math. Notes, 93:4 (2013), 545–555
Citation in format AMSBIB
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  • https://doi.org/10.4213/mzm9023
  • https://www.mathnet.ru/eng/mzm/v93/i4/p537
    • This publication is cited in the following 4 articles:
    1. D. B. Davletov, O. B. Davletov, R. R. Davletova, A. A. Ershov, “O sobstvennykh elementakh dvumernoi kraevoi zadachi tipa Steklova dlya operatora Lame”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 33:1 (2023), 54–65  mathnet  crossref  mathscinet
    2. D. B. Davletov, O. B. Davletov, R. R. Davletova, A. A. Ershov, “Skhodimost sobstvennykh elementov kraevoi zadachi tipa Steklova dlya operatora Lame”, Tr. IMM UrO RAN, 27, no. 1, 2021, 37–47  mathnet  crossref  elib
    3. D. B. Davletov, O. B. Davletov, “Convergence of eigenelements of a Steklov-type problem in a half-band with a small hole”, J. Math. Sci. (N. Y.), 241:5 (2019), 549–555  mathnet  mathnet  crossref
    4. D. B. Davletov, D. V. Kozhevnikov, “The problem of Steklov type in a half-cylinder with a small cavity”, Ufa Math. J., 8:4 (2016), 62–87  mathnet  crossref  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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