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Mat. Sb., 2012, Volume 203, Number 5, Pages 135–160 (Mi msb7844)  

This article is cited in 11 scientific papers (total in 11 papers)

Bounded and periodic solutions of nonlinear functional differential equations

V. E. Slyusarchuk

Ukranian State Academy of Water Economy

Abstract: Conditions for the existence of bounded and periodic solutions of the nonlinear functional differential equation
$$ \frac{d^mx(t)}{dt^m}+(Fx)(t)=h(t), \qquad t\in \mathbb{R}, $$
are presented, involving local linear approximations to the operator $F$.
Bibliography: 23 titles.

Keywords: bounded and periodic solutions, nonlinear functional differential equations, invertibility of linear operators.

DOI: https://doi.org/10.4213/sm7844

Full text: PDF file (635 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2012, 203:5, 743–767

Bibliographic databases:

UDC: 517.988.6
MSC: 34K12, 34K13
Received: 17.01.2011

Citation: V. E. Slyusarchuk, “Bounded and periodic solutions of nonlinear functional differential equations”, Mat. Sb., 203:5 (2012), 135–160; Sb. Math., 203:5 (2012), 743–767

Citation in format AMSBIB
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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. Slyusarchuk V.Yu., “A Method of Local Linear Approximation For the Nonlinear Discrete Equations”, Ukr. Math. J.  crossref  mathscinet  isi
    2. J. Math. Sci. (N. Y.), 194:4 (2013), 440–452  crossref  mathscinet  zmath  scopus
    3. V. Yu. Slyusarchuk, “Conditions for the existence of almost periodic solutions of nonlinear differential equations in Banach spaces”, Ukr. Math. J., 65:2 (2013), 341–347  crossref  mathscinet  zmath  isi  scopus
    4. J. Math. Sci. (N. Y.), 197:1 (2014), 122–128  crossref  mathscinet  zmath  scopus
    5. 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
    6. V. E. Slyusarchuk, “Conditions for almost periodicity of bounded solutions of non-linear differential-difference equations”, Izv. Math., 78:6 (2014), 1232–1243  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    7. V. Yu. Slyusarchuk, “Conditions for almost periodicity of bounded solutions of nonlinear differential equations unsolved with respect to the derivative”, Ukr. Math. J., 66:3 (2014), 432–442  crossref  mathscinet  zmath  isi  scopus
    8. V. E. Slyusarchuk, “Conditions for the Existence of Almost-Periodic Solutions of Nonlinear Difference Equations in Banach Space”, Math. Notes, 97:2 (2015), 268–274  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    9. V. Yu. Slyusarchuk, “Conditions of solvability for nonlinear differential equations with perturbations of the solutions in the space of functions bounded on the axis”, Ukrainian Math. J., 68:9 (2017), 1481–1493  crossref  mathscinet  zmath  isi  scopus
    10. V. Yu. Slyusarchuk, “Necessary and sufficient conditions for the invertibility of nonlinear differentiable maps”, Ukrainian Math. J., 68:4 (2016), 638–652  crossref  mathscinet  zmath  isi  scopus
    11. V. Yu. Slyusarchuk, “Favard-Amerio theory for almost periodic functional-differential equations without using the $\mathcal H$-classes of those equations”, Ukrainian Math. J., 69:6 (2017), 916–932  crossref  mathscinet  zmath  isi  scopus
  • Математический сборник Sbornik: Mathematics (from 1967)
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