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Mathematics of the USSR-Sbornik, 1973, Volume 19, Issue 2, Pages 209–223
DOI: https://doi.org/10.1070/SM1973v019n02ABEH001746
(Mi sm3007)
 

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

Monotonicity in the theory of almost periodic solutions of nonlinear operator equations

V. V. Zhikov
References:
Abstract: In a Banach space with a strictly convex norm we consider a nonlinear equation $u'+A(t)u=0$ of general form. Suppose that a “monotonicity” condition is satisfied: for any two solutions $u_1(t)$ and $u_2(t)$ the function $g(t)=\|u_1(t)-u_2(t)\|$ is nonincreasing with respect to $t$; suppose $A(t)$ is almost periodic (in some sense) with respect to $t$.
The basic theorem reads as follows: given strong (weak) continuity of the solutions with respect to the initial conditions and the coefficients, there exists at least one almost periodic solution if there exists a compact (weakly compact) solution on $t\geqslant0$.
Bibliography: 26 titles.
Received: 21.06.1972
Bibliographic databases:
UDC: 519.4+517+513.88
MSC: Primary 47H15, 34C25, 34G05; Secondary 34H05, 47H10
Language: English
Original paper language: Russian
Citation: V. V. Zhikov, “Monotonicity in the theory of almost periodic solutions of nonlinear operator equations”, Math. USSR-Sb., 19:2 (1973), 209–223
Citation in format AMSBIB
\Bibitem{Zhi73}
\by V.~V.~Zhikov
\paper Monotonicity in the theory of almost periodic solutions of nonlinear operator equations
\jour Math. USSR-Sb.
\yr 1973
\vol 19
\issue 2
\pages 209--223
\mathnet{http://mi.mathnet.ru//eng/sm3007}
\crossref{https://doi.org/10.1070/SM1973v019n02ABEH001746}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=341221}
\zmath{https://zbmath.org/?q=an:0259.34071}
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  • https://doi.org/10.1070/SM1973v019n02ABEH001746
  • https://www.mathnet.ru/eng/sm/v132/i2/p214
  • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics
    Statistics & downloads:
    Abstract page:585
    Russian version PDF:194
    English version PDF:7
    References:46
     
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