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Matematicheskie Zametki, 1971, Volume 9, Issue 4, Pages 409–414 (Mi mzm7023)  
This article is cited in 6 scientific papers (total in 6 papers)

The existence of Levitan almost-periodic solutions of linear systems (second complement to Favard's classical theory)

V. V. Zhikov

Vladimir Polytechnical Institute
Full-text PDF (504 kB) Citations (6)
Abstract: The linear equation $u'=A(t)u+f(t)$ with almost periodic coefficients is investigated in euclidean space. It is proved that if it has a bounded solution, then it has a Levitan almost-periodic function as a “limit” solution.
Received: 14.12.1969
English version:
Mathematical Notes, 1971, Volume 9, Pages 235–238
DOI: https://doi.org/10.1007/BF01387771
Bibliographic databases:
UDC: 513.88
Language: Russian
Citation: V. V. Zhikov, “The existence of Levitan almost-periodic solutions of linear systems (second complement to Favard's classical theory)”, Mat. Zametki, 9:4 (1971), 409–414; Math. Notes, 9 (1971), 235–238
Citation in format AMSBIB
\Bibitem{Zhi71}
\by V.~V.~Zhikov
\paper The existence of Levitan almost-periodic solutions of linear systems (second complement to Favard's classical theory)
\jour Mat. Zametki
\yr 1971
\vol 9
\issue 4
\pages 409--414
\mathnet{http://mi.mathnet.ru/mzm7023}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=282006}
\zmath{https://zbmath.org/?q=an:0235.34095|0224.34036}
\transl
\jour Math. Notes
\yr 1971
\vol 9
\pages 235--238
\crossref{https://doi.org/10.1007/BF01387771}
Linking options:
  • https://www.mathnet.ru/eng/mzm7023
  • https://www.mathnet.ru/eng/mzm/v9/i4/p409
    • This publication is cited in the following 6 articles:
    1. David N. Cheban, Monotone Nonautonomous Dynamical Systems, 2024, 221  crossref
    2. David Cheban, “Levitan almost periodic solutions of infinite-dimensional linear differential equations”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2019, no. 2, 56–78  mathnet
    3. V. E. Slyusarchuk, “The study of nonlinear almost periodic differential equations without recourse to the $\mathscr H$-classes of these equations”, Sb. Math., 205:6 (2014), 892–911  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. V. E. Slyusarchuk, “Invertibility of almost periodic $c$-continuous functional operators”, Math. USSR-Sb., 44:4 (1983), 431–446  mathnet  crossref  mathscinet  zmath
    5. M. A. Shubin, “Almost periodic functions and partial differential operators”, Russian Math. Surveys, 33:2 (1978), 1–52  mathnet  crossref  mathscinet  zmath
    6. V. V. Zhikov, B. M. Levitan, “Favard theory”, Russian Math. Surveys, 32:2 (1977), 129–180  mathnet  crossref  mathscinet  zmath
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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