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

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

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

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

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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
2. R. R. Gadyl'shin, “On eigenfrequencies of bodies with thin branches. II. Asymptotics”, Math. Notes, 55:1 (1994), 14–23
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
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
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
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
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
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
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
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
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
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
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
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
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
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
17. Melikhova A.S. Popov I.Yu., “Spectral problem for solvable model of bent nano peapod”, Appl. Anal., 96:2 (2017), 215–224
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