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Izv. Akad. Nauk SSSR Ser. Mat., 1976, Volume 40, Issue 6, Pages 1380–1408 (Mi izv2263)  

This article is cited in 26 scientific papers (total in 26 papers)

Some admissibility and dichotomy questions. The averaging principle

V. V. Zhikov


Abstract: In this paper some questions in the general theory of stability are studied, with a subsequent application to the problem of averaging on the whole axis.
Bibliography: 14 titles.

Full text: PDF file (2678 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Izvestiya, 1976, 10:6, 1307–1332

Bibliographic databases:

UDC: 519.4+513.88
MSC: 34A10, 34C30, 34G05
Received: 22.04.1974

Citation: V. V. Zhikov, “Some admissibility and dichotomy questions. The averaging principle”, Izv. Akad. Nauk SSSR Ser. Mat., 40:6 (1976), 1380–1408; Math. USSR-Izv., 10:6 (1976), 1307–1332

Citation in format AMSBIB
\Bibitem{Zhi76}
\by V.~V.~Zhikov
\paper Some admissibility and dichotomy questions. The averaging principle
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1976
\vol 40
\issue 6
\pages 1380--1408
\mathnet{http://mi.mathnet.ru/izv2263}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=508720}
\zmath{https://zbmath.org/?q=an:0357.34040}
\transl
\jour Math. USSR-Izv.
\yr 1976
\vol 10
\issue 6
\pages 1307--1332
\crossref{https://doi.org/10.1070/IM1976v010n06ABEH001836}


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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. V. V. Zhikov, B. M. Levitan, “Favard theory”, Russian Math. Surveys, 32:1 (1977), 129–180  mathnet  crossref  mathscinet  zmath
    2. V. V. Zhikov, S. M. Kozlov, O. A. Oleinik, “$G$-convergence of parabolic operators”, Russian Math. Surveys, 36:1 (1981), 9–60  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. A. A. Pankov, “Boundedness and almost periodicity in time of solutions of evolutionary variational inequalities”, Math. USSR-Izv., 20:2 (1983), 303–332  mathnet  crossref  mathscinet  zmath
    4. V. V. Zhikov, S. M. Kozlov, O. A. Oleinik, “Averaging of parabolic operators with almost periodic coefficients”, Math. USSR-Sb., 45:1 (1983), 73–90  mathnet  crossref  mathscinet  zmath
    5. V. B. Levenshtam, “Averaging of quasilinear parabolic equations with rapidly oscillating principal part. Exponential dichotomy”, Russian Acad. Sci. Izv. Math., 41:1 (1993), 95–132  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    6. A. A. Ilyin, “Averaging principle for dissipative dynamical systems with rapidly oscillating right-hand sides”, Sb. Math., 187:5 (1996), 635–677  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    7. V. M. Tyurin, “On the invertibility of linear differential operators with a closed range and with Poisson coefficients”, Math. Notes, 65:1 (1999), 120–123  mathnet  crossref  crossref  mathscinet  zmath  isi
    8. A. G. Baskakov, “On correct linear differential operators”, Sb. Math., 190:3 (1999), 323–348  mathnet  crossref  crossref  mathscinet  zmath  isi
    9. A. G. Baskakov, “Invertibility and the Fredholm property of difference operators”, Math. Notes, 67:6 (2000), 690–698  mathnet  crossref  crossref  mathscinet  zmath  isi
    10. V. M. Tyurin, “Generalized Admissibility, Well-Definedness, and Invertibility of Linear Partial Differential Operators”, Proc. Steklov Inst. Math., 236 (2002), 330–333  mathnet  mathscinet  zmath
    11. V. M. Tyurin, “On the Equivalence of Spectra of Linear Partial Differential Operators in Certain Function Spaces”, Math. Notes, 72:6 (2002), 833–840  mathnet  crossref  crossref  mathscinet  zmath  isi
    12. V. B. Levenshtam, “Unique Solvability of Parabolic Equations with Almost-Periodic Coefficients in Hölder Spaces”, Math. Notes, 73:6 (2003), 813–828  mathnet  crossref  crossref  mathscinet  zmath  isi
    13. O. A. Mitina, V. M. Tyurin, “On invertibility of linear partial differential operators in Hölder and Sobolev spaces”, Sb. Math., 194:5 (2003), 733–744  mathnet  crossref  crossref  mathscinet  zmath  isi
    14. A. G. Baskakov, “Representation theory for Banach algebras, Abelian groups, and semigroups in the spectral analysis of linear operators”, Journal of Mathematical Sciences, 137:4 (2006), 4885–5036  mathnet  crossref  mathscinet  zmath  elib
    15. Baskakov A.G., Krishtal I.A., “Spectral analysis of operators with the two-point Bohr spectrum”, Journal of Mathematical Analysis and Applications, 308:2 (2005), 420–439  crossref  isi  elib
    16. V. B. Levenshtam, “Uniform exponential dichotomy of parabolic operators with rapidly oscillating coefficients”, Math. Notes, 79:5 (2006), 675–680  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    17. A. G. Baskakov, “Spectral analysis of differential operators with unbounded operator-valued coefficients, difference relations and semigroups of difference relations”, Izv. Math., 73:2 (2009), 215–278  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    18. T. B. Kuznetsova, V. M. Tyurin, “Ob obratimosti lineinykh differentsialnykh operatorov ellipticheskogo tipa v nekotorykh funktsionalnykh prostranstvakh”, Vestn. SamGU. Estestvennonauchn. ser., 2009, no. 4(70), 5–19  mathnet
    19. M. S. Bichegkuev, “O spektre raznostnykh i differentsialnykh operatorov v vesovykh prostranstvakh”, Funkts. analiz i ego pril., 44:1 (2010), 80–83  mathnet  crossref  mathscinet  zmath
    20. M. S. Bichegkuev, S. V. Besaeva, “Spectral properties of difference and differential operators in weighted spaces”, Russian Math. (Iz. VUZ), 55:2 (2011), 13–17  mathnet  crossref  mathscinet  elib
    21. M. S. Bichegkuev, “On conditions for invertibility of difference and differential operators in weight spaces”, Izv. Math., 75:4 (2011), 665–680  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    22. Nazaruk E.M., Romanovskaya A.M., “Ob eksponentsialnoi dikhotomii reshenii zadachi koshi dlya sistemy differentsialno-raznostnykh uravnenii s postoyannymi koeffitsientami”, Vestnik omskogo universiteta, 2011, no. 4, 45–49  elib
    23. A. G. Baskakov, “Analysis of linear differential equations by methods of the spectral theory of difference operators and linear relations”, Russian Math. Surveys, 68:1 (2013), 69–116  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    24. R. K. Romanovskii, E. M. Nazaruk, “On the Dichotomy of Linear Autonomous Systems of Functional-Differential Equations”, Math. Notes, 95:1 (2014), 116–121  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    25. Romanovskii R.K., Nazaruk E.M., “Dichotomy of Solutions of Functional-Differential Equations in the Sobolev Space”, Differ. Equ., 51:4 (2015), 464–476  crossref  isi
    26. L. I. Sazonov, “High-frequency asymptotics of solutions of ODE in a Banach space”, Izv. Math., 81:6 (2017), 1234–1252  mathnet  crossref  crossref  adsnasa  isi  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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