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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 W21(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/sjim803
  • 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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