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Mat. Sb., 1990, Volume 181, Number 12, Pages 1678–1693 (Mi msb1254)  

This article is cited in 15 scientific papers (total in 16 papers)

Spectral asymptotics of nonselfadjoint elliptic systems of differential operators on bounded domains

K. Kh. Boimatova, A. G. Kostyuchenkob

a Institute of Mathematics with Computing Centre, Republic of Tajikistan Academy of Sciences
b M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: In a bounded domain $\Omega\subset R_n$ with smooth boundary, a matrix elliptic differential operator $A$ is considered. It is assumed that the eigenvalues of the symbol of $A$ lie on the positive semiaxis $R^+$ and outside the angle $\Phi=ż\colon|\arg z|\leqslant\varphi\}$, $\varphi\in(0,\pi)$.

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English version:
Mathematics of the USSR-Sbornik, 1992, 71:2, 517–531

Bibliographic databases:

UDC: 517.9
MSC: 35J45, 35P20
Received: 10.10.1989

Citation: K. Kh. Boimatov, A. G. Kostyuchenko, “Spectral asymptotics of nonselfadjoint elliptic systems of differential operators on bounded domains”, Mat. Sb., 181:12 (1990), 1678–1693; Math. USSR-Sb., 71:2 (1992), 517–531

Citation in format AMSBIB
\by K.~Kh.~Boimatov, A.~G.~Kostyuchenko
\paper Spectral asymptotics of nonselfadjoint elliptic systems of differential operators on bounded domains
\jour Mat. Sb.
\yr 1990
\vol 181
\issue 12
\pages 1678--1693
\jour Math. USSR-Sb.
\yr 1992
\vol 71
\issue 2
\pages 517--531

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    This publication is cited in the following articles:
    1. K. Kh. Boimatov, “The spectral asymptotics of pseudodifferential systems elliptic in the sense of Douglis and Nirenberg”, Russian Math. Surveys, 46:5 (1991), 183–184  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. M. S. Agranovich, “On modules of eigenvalues for non-self-adjoint agmon–Douglis–Nirenberg elliptic boundary problems with a parameter”, Funct. Anal. Appl., 26:2 (1992), 116–119  mathnet  crossref  mathscinet  zmath  isi
    3. Boimatov K., “Spectral Asymptotics of Linear and Nonlinear Pencils of Douglis-Nirenberg Elliptic Pseudodifferential-Operators”, 322, no. 3, 1992, 441–445  mathscinet  isi
    4. Boimatov K., “Spectral Asymptotic of Nonself-Adjoint Degenerate Elliptic-Systems of Differential-Operators”, Dokl. Akad. Nauk, 330:5 (1993), 533–538  mathnet  mathscinet  isi
    5. K. Kh. Boimatov, “Some Spectral Properties of Matrix Differential Operators Far from Being Self-Adjoint”, Funct. Anal. Appl., 29:3 (1995), 191–193  mathnet  crossref  mathscinet  zmath  isi
    6. Boimatov K., “Some Asymptotical Formulas for the Elliptic Operations in R(N), That Are Far From Selfadjointness”, Dokl. Akad. Nauk, 344:6 (1995), 730–735  mathnet  mathscinet  zmath  isi
    7. A. Sameripour, K. Seddighi, “Distribution of eigenvalues of nonself-adjoint elliptic systems degenerate on the domain boundary”, Math. Notes, 61:3 (1997), 379–384  mathnet  crossref  crossref  mathscinet  zmath  isi
    8. Boimatov K., Seddighi K., “Some Spectral Properties of Ordinary Differential Operators Associated with Noncoercive Forms”, Dokl. Akad. Nauk, 352:4 (1997), 439–442  mathnet  mathscinet  isi
    9. Boimatov K., “On Spectral Asymptotics and Abel Summability of Series Over Systems of Root Vector-Functions of Nonsmooth Elliptic Differential Operators Far From Self-Adjoint”, Dokl. Math., 61:3 (2000), 376–379  zmath  isi
    10. V. V. Pod'yapol'skii, “Completeness of the Root Function System of a Nonlocal Problem in $L_p$”, Math. Notes, 71:6 (2002), 804–814  mathnet  crossref  crossref  mathscinet  zmath  isi
    11. M. G. Gadoev, “Asymptotics of the spectrum of second-order nonselfadjoint degenerate elliptic differential operators on an interval”, J. Appl. Industr. Math., 2:1 (2008), 57–67  mathnet  crossref  mathscinet  elib
    12. Kostyuchenko A.G., “Spectral asymptotics of a nonself-adjoint elliptic differential operator with an indefinite weight function”, Differ. Equ., 45:4 (2009), 549–557  crossref  mathscinet  zmath  isi  elib  elib
    13. M. S. Agranovich, V. M. Buchstaber, R. S. Ismagilov, B. S. Kashin, B. S. Mityagin, S. P. Novikov, V. A. Sadovnichii, A. G. Sergeev, Ya. G. Sinai, A. A. Shkalikov, “Anatolii Gordeevich Kostyuchenko (obituary)”, Russian Math. Surveys, 65:4 (2010), 767–780  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    14. M. G. Gadoev, “Spektralnaya asimptotika nesamosopryazhennykh vyrozhdayuschikhsya ellipticheskikh operatorov s singulyarnymi matrichnymi koeffitsientami na otrezke”, Ufimsk. matem. zhurn., 3:3 (2011), 26–54  mathnet  zmath
    15. Lakshtanov E., Vainberg B., “Bounds on Positive Interior Transmission Eigenvalues”, Inverse Probl., 28:10 (2012), 105005  crossref  mathscinet  zmath  adsnasa  isi
    16. M. G. Gadoev, S. A. Iskhokov, “Spectral properties of degenerate elliptic operators with matrix coefficients”, Ufa Math. J., 5:4 (2013), 37–48  mathnet  crossref  elib
  • Математический сборник - 1989–1990 Sbornik: Mathematics (from 1967)
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