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Differ. Uravn., 1999, Volume 35, Number 4, Pages 540–551 (Mi de9364)  

This article is cited in 12 scientific papers (total in 12 papers)

Partial Differential Equations

Asymptotics of the eigenvalues of a boundary value problem with rapidly oscillating boundary conditions

R. R. Gadyl'shin

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

Full text: PDF file (1769 kB)

English version:
Differential Equations, 1999, 35:4, 540–551

Bibliographic databases:
UDC: 517.956.22
Received: 26.05.1997

Citation: R. R. Gadyl'shin, “Asymptotics of the eigenvalues of a boundary value problem with rapidly oscillating boundary conditions”, Differ. Uravn., 35:4 (1999), 540–551; Differ. Equ., 35:4 (1999), 540–551

Citation in format AMSBIB
\Bibitem{Gad99}
\by R.~R.~Gadyl'shin
\paper Asymptotics of the eigenvalues of a boundary value problem with rapidly oscillating boundary conditions
\jour Differ. Uravn.
\yr 1999
\vol 35
\issue 4
\pages 540--551
\mathnet{http://mi.mathnet.ru/de9364}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1719780}
\transl
\jour Differ. Equ.
\yr 1999
\vol 35
\issue 4
\pages 540--551


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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, “Homogenization and asymptotics for a membrane with closely spaced clamping points”, Comput. Math. Math. Phys., 41:12 (2001), 1765–1776  mathnet  mathscinet  zmath  elib
    2. D. I. Borisov, “Boundary-value problem in a cylinder with frequently changing type of boundary”, Sb. Math., 193:7 (2002), 977–1008  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. D. I. Borisov, “Asymptotics and estimates for the eigenelements of the Laplacian with frequently alternating non-periodic boundary conditions”, Izv. Math., 67:6 (2003), 1101–1148  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. D. I. Borisov, “Asymptotics and estimates of the convergence rate in a three-dimensional boundary-value problem with rapidly alternating boundary conditions”, Siberian Math. J., 45:2 (2004), 222–240  mathnet  crossref  mathscinet  zmath  isi  elib
    5. 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
    6. D. I. Borisov, “On a problem with nonperiodic frequent alternation of boundary conditions imposed on fast oscillating sets”, Comput. Math. Math. Phys., 46:2 (2006), 271–281  mathnet  crossref  mathscinet  zmath  elib  elib
    7. V. A. Sadovnichii, A. G. Chechkina, “Ob otsenke sobstvennykh funktsii zadachi tipa Steklova s malym parametrom v sluchae predelnogo vyrozhdeniya spektra”, Ufimsk. matem. zhurn., 3:3 (2011), 127–139  mathnet  zmath
    8. T. F. Sharapov, “On the resolvent of multidimensional operators with frequently changing boundary conditions in the case of the homogenized Dirichlet condition”, Sb. Math., 205:10 (2014), 1492–1527  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    9. A. G. Chechkina, V. A. Sadovnichy, “Degeneration of Steklovtype boundary conditions in one spectral homogenization problem”, Eurasian Math. J., 6:3 (2015), 13–29  mathnet
    10. R. R. Gadyl'shin, S. V. Repjevskij, E. A. Shishkina, “On an eigenvalue for the Laplace operator in a disk with Dirichlet boundary condition on a small part of the boundary in a critical case”, Proc. Steklov Inst. Math. (Suppl.), 292, suppl. 1 (2016), 76–90  mathnet  crossref  mathscinet  elib
    11. T. F. Sharapov, “On resolvent of multi-dimensional operators with frequent alternation of boundary conditions: critical case”, Ufa Math. J., 8:2 (2016), 65–94  mathnet  crossref  elib
    12. R. R. Gadyl'shin, A. L. Piatnitski, G. A. Chechkin, “On the asymptotic behaviour of eigenvalues of a boundary-value problem in a planar domain of Steklov sieve type”, Izv. Math., 82:6 (2018), 1108–1135  mathnet  crossref  crossref  adsnasa  isi  elib
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