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Mat. Zametki, 1971, Volume 9, Issue 4, Pages 409–414 (Mi mz7023)  

This article is cited in 5 scientific papers (total in 5 papers)

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

V. V. Zhikov

Vladimir Polytechnical Institute

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.

Full text: PDF file (504 kB)

English version:
Mathematical Notes, 1971, 9, 235–238

Bibliographic databases:

UDC: 513.88
Received: 14.12.1969

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/mz7023}
\mathscinet{http://www.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}


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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. M. A. Shubin, “Almost periodic functions and partial differential operators”, Russian Math. Surveys, 33:2 (1978), 1–52  mathnet  crossref  mathscinet  zmath
    3. V. E. Slyusarchuk, “Invertibility of almost periodic $c$-continuous functional operators”, Math. USSR-Sb., 44:4 (1983), 431–446  mathnet  crossref  mathscinet  zmath
    4. 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
    5. David Cheban, “Levitan almost periodic solutions of infinite-dimensional linear differential equations”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2019, no. 2, 56–78  mathnet
  • Математические заметки Mathematical Notes
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