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Mat. Zametki, 1992, Volume 52, Issue 4, Pages 42–55 (Mi mz4754)  

This article is cited in 17 scientific papers (total in 17 papers)

Ramification of a multiple eigenvalue of the Dirichlet problem for the Laplacian under singular perturbation of the boundary condition

R. R. Gadyl'shin

Institute of Mathematics and Computing Centre of Ural Branch of Russian Academy of Sciences

Full text: PDF file (1389 kB)

English version:
Mathematical Notes, 1992, 52:4, 1020–1029

Bibliographic databases:

Received: 19.09.1991

Citation: R. R. Gadyl'shin, “Ramification of a multiple eigenvalue of the Dirichlet problem for the Laplacian under singular perturbation of the boundary condition”, Mat. Zametki, 52:4 (1992), 42–55; Math. Notes, 52:4 (1992), 1020–1029

Citation in format AMSBIB
\Bibitem{Gad92}
\by R.~R.~Gadyl'shin
\paper Ramification of a multiple eigenvalue of the Dirichlet problem for the Laplacian under singular perturbation of the boundary condition
\jour Mat. Zametki
\yr 1992
\vol 52
\issue 4
\pages 42--55
\mathnet{http://mi.mathnet.ru/mz4754}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1203951}
\zmath{https://zbmath.org/?q=an:0816.35093}
\transl
\jour Math. Notes
\yr 1992
\vol 52
\issue 4
\pages 1020--1029
\crossref{https://doi.org/10.1007/BF01210435}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1992LF91500024}


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

    This publication is cited in the following articles:
    1. R. R. Gadyl'shin, “Characteristic frequencies of bodies with thin spikes. I. Convergence and estimates”, Math. Notes, 54:6 (1993), 1192–1199  mathnet  crossref  mathscinet  zmath  isi
    2. R. R. Gadyl'shin, “On eigenfrequencies of bodies with thin branches. II. Asymptotics”, Math. Notes, 55:1 (1994), 14–23  mathnet  crossref  mathscinet  zmath  isi  elib
    3. R. R. Gadyl'shin, “On the perturbation of the Laplacian spectrum when the boundary condition type changes on a small part of the boundary”, Comput. Math. Math. Phys., 36:7 (1996), 889–898  mathnet  mathscinet  zmath  isi
    4. R. R. Gadyl'shin, “Existence and asymptotics of poles with small imaginary part for the Helmholtz resonator”, Russian Math. Surveys, 52:1 (1997), 1–72  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    5. R. R. Gadyl'shin, A. M. Il'in, “Asymptotic behaviour of the eigenvalues of the Dirichlet problem in a domain with a narrow slit”, Sb. Math., 189:4 (1998), 503–526  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    6. Planida, MY, “Asymptotics for eigenvalues of the Laplacian with a Neumann boundary condition on a thin cut-out tube”, Comptes Rendus Mecanique, 331:8 (2003), 531  crossref  adsnasa  isi
    7. M. Yu. Planida, “Asymptotics of the Eigenelements of the Laplace Operator when the Boundary-Condition Type Changes on a Narrow Flattened Strip”, Math. Notes, 75:2 (2004), 213–228  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    8. G. A. Chechkin, “Asymptotic expansions of eigenvalues and eigenfunctions of an elliptic operator in a domain with many “light” concentrated masses situated on the boundary. Two-dimensional case”, Izv. Math., 69:4 (2005), 805–846  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    9. M. I. Cherdantsev, “Asymptotic Expansion of Eigenvalues of the Laplace Operator in Domains with Singularly Perturbed Boundary”, Math. Notes, 78:2 (2005), 270–278  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    10. M. Yu. Planida, “Asymptotics of the eigenelements of the Laplacian with singular perturbations of boundary conditions on narrow and thin sets”, Sb. Math., 196:5 (2005), 703–741  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    11. A. R. Bikmetov, D. I. Borisov, “Discrete Spectrum of the Schrodinger Operator Perturbed by a Narrowly Supported Potential”, Theoret. and Math. Phys., 145:3 (2005), 1691–1702  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    12. D. B. Davletov, “Asymptotics of eigenvalues of the Dirichlet boundary value problem for the Lame operator in a three-dimensional domain with a small cavity”, Comput. Math. Math. Phys., 48:10 (2008), 1811–1822  mathnet  crossref  mathscinet  zmath  isi
    13. R. R. Gadyl'shin, E. A. Shishkina, “On Friedrichs inequalities for a disk”, Proc. Steklov Inst. Math. (Suppl.), 281, suppl. 1 (2013), 44–58  mathnet  crossref  isi  elib
    14. D. I. Borisov, K. V. Pankrashin, “Gap Opening and Split Band Edges in Waveguides Coupled by a Periodic System of Small Windows”, Math. Notes, 93:5 (2013), 660–675  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    15. R. R. Gadylshin, A. A. Ershov, S. V. Repyevsky, “On asymptotic formula for electric resistance of conductor with small contacts”, Ufa Math. J., 7:3 (2015), 15–27  mathnet  crossref  isi  elib
    16. Borisov D.I., “on the Band Spectrum of a Schrodinger Operator in a Periodic System of Domains Coupled By Small Windows”, Russ. J. Math. Phys., 22:2 (2015), 153–160  crossref  isi
    17. Melikhova A.S. Popov I.Yu., “Spectral problem for solvable model of bent nano peapod”, Appl. Anal., 96:2 (2017), 215–224  crossref  mathscinet  zmath  isi  elib  scopus
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