RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Sb.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Mat. Sb. (N.S.), 1973, Volume 90(132), Number 2, Pages 214–228 (Mi msb3007)  

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


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.

Full text: PDF file (1616 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Sbornik, 1973, 19:2, 209–223

Bibliographic databases:

UDC: 519.4+517+513.88
MSC: Primary 47H15, 34C25, 34G05; Secondary 34H05, 47H10
Received: 21.06.1972

Citation: V. V. Zhikov, “Monotonicity in the theory of almost periodic solutions of nonlinear operator equations”, Mat. Sb. (N.S.), 90(132):2 (1973), 214–228; 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 Mat. Sb. (N.S.)
\yr 1973
\vol 90(132)
\issue 2
\pages 214--228
\mathnet{http://mi.mathnet.ru/msb3007}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=341221}
\zmath{https://zbmath.org/?q=an:0259.34071}
\transl
\jour Math. USSR-Sb.
\yr 1973
\vol 19
\issue 2
\pages 209--223
\crossref{https://doi.org/10.1070/SM1973v019n02ABEH001746}


Linking options:
  • http://mi.mathnet.ru/eng/msb3007
  • http://mi.mathnet.ru/eng/msb/v132/i2/p214

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. A. A. Pankov, “Bounded and almost periodic solutions of evolutionary variational inequalities”, Math. USSR-Sb., 36:4 (1980), 519–533  mathnet  crossref  mathscinet  zmath  isi
    3. A. A. Pankov, “Boundedness and almost periodicity in time of solutions of evolutionary variational inequalities”, Math. USSR-Izv., 20:2 (1983), 303–332  mathnet  crossref  mathscinet  zmath
    4. D. N. Cheban, “Bounded solutions of linear almost periodic differential equations”, Izv. Math., 62:3 (1998), 581–600  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. David N. Cheban, Peter E. Kloeden, Björn Schmalfuß, “Global attractors for $V$-monotone nonautonomous dynamical systems”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2003, no. 1, 47–57  mathnet  mathscinet  zmath
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
    Number of views:
    This page:425
    Full text:118
    References:28

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019