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Sibirskii Zhurnal Industrial'noi Matematiki, 2013, Volume 16, Number 4, Pages 38–46 (Mi sjim803)  
This article is cited in 5 scientific papers (total in 5 papers)

Systems of differential equations with periodic coefficients

G. V. Demidenkoab

a Sobolev Institute of Mathematics SB RAS, 4 Koptyug av., 630090 Novosibirsk
b Novosibirsk State University, 2 Pirogov st., 630090 Novosibirsk
Full-text PDF (212 kB) Citations (5)
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Abstract: We consider linear systems of differential equations with periodic coefficients. We prove the solvability of nonhomogeneous systems in the Sobolev space $W^1_2(R)$ and establish the estimates for the solutions. Using the result, we prove a theorem on a perturbation for the exponential dichotomy of systems of differential equations with periodic coefficients.
Keywords: exponential dichotomy, periodic coefficients, perturbation, projection, Green matrix, Sobolev space.
Received: 22.07.2013
English version:
Journal of Applied and Industrial Mathematics, 2014, Volume 8, Issue 1, Pages 20–27
DOI: https://doi.org/10.1134/S1990478914010037
Bibliographic databases:
Document Type: Article
UDC: 517.925.51
Language: Russian
Citation: G. V. Demidenko, “Systems of differential equations with periodic coefficients”, Sib. Zh. Ind. Mat., 16:4 (2013), 38–46; J. Appl. Industr. Math., 8:1 (2014), 20–27
Citation in format AMSBIB
\Bibitem{Dem13}
\by G.~V.~Demidenko
\paper Systems of differential equations with periodic coefficients
\jour Sib. Zh. Ind. Mat.
\yr 2013
\vol 16
\issue 4
\pages 38--46
\mathnet{http://mi.mathnet.ru/sjim803}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3234791}
\transl
\jour J. Appl. Industr. Math.
\yr 2014
\vol 8
\issue 1
\pages 20--27
\crossref{https://doi.org/10.1134/S1990478914010037}
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  • https://www.mathnet.ru/eng/sjim/v16/i4/p38
    • This publication is cited in the following 5 articles:
    1. G. V. Demidenko, A. A. Bondar, M. Sh. Ganzhaeva, “Eksponentsialnaya dikhotomiya sistem raznostnykh uravnenii pri vozmuschenii koeffitsientov”, Chelyab. fiz.-matem. zhurn., 9:4 (2024), 561–572  mathnet  crossref
    2. G. V. Demidenko, “On one class of systems of differential equations with periodic coefficients in linear terms”, Siberian Math. J., 62:5 (2021), 805–821  mathnet  crossref  crossref  isi  elib
    3. M. V. Falaleev, E. Y. Grazhdantseva, “Generalized Solutions of Differential Equations with the Derivatives of Functionals in Banach Spaces”, Lobachevskii J Math, 42:15 (2021), 3626  crossref
    4. G. V. Demidenko, “On the Existence of Periodic Solutions to One Class of Systems of Nonlinear Differential Equations”, Lobachevskii J Math, 42:14 (2021), 3336  crossref
    5. G. V. Demidenko, “On conditions for exponential dichotomy of systems of linear differential equations with periodic coefficients”, Int. J. Dyn. Syst. Differ. Equ., 6:1 (2016), 63–74  crossref  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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