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Mat. Sb., 2014, Volume 205, Number 6, Pages 139–160 (Mi msb8188)  

This article is cited in 7 scientific papers (total in 7 papers)

The study of nonlinear almost periodic differential equations without recourse to the $\mathscr H$-classes of these equations

V. E. Slyusarchuk

Ukranian State Academy of Water Economy, Rivne

Abstract: The well-known theorems of Favard and Amerio on the existence of almost periodic solutions to linear and nonlinear almost periodic differential equations depend to a large extent on the $\mathscr H$-classes and the requirement that the bounded solutions of these equations be separated. The present paper provides different conditions for the existence of almost periodic solutions. These conditions, which do not depend on the $\mathscr H$-classes of the equations, are formulated in terms of a special functional on the set of bounded solutions of the equations under consideration. This functional is used, in particular, to test whether solutions are separated.
Bibliography: 24 titles.

Keywords: bounded and almost periodic solution, nonlinear almost periodic differential equations, Amerio's theorem.

DOI: https://doi.org/10.4213/sm8188

Full text: PDF file (576 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2014, 205:6, 892–911

Bibliographic databases:

UDC: 517.925.52
MSC: 34C27
Received: 02.11.2012 and 01.01.2014

Citation: V. E. Slyusarchuk, “The study of nonlinear almost periodic differential equations without recourse to the $\mathscr H$-classes of these equations”, Mat. Sb., 205:6 (2014), 139–160; Sb. Math., 205:6 (2014), 892–911

Citation in format AMSBIB
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  • https://doi.org/10.4213/sm8188
  • http://mi.mathnet.ru/eng/msb/v205/i6/p139

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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., “On the Favard Theory Without H-Classes For Differential-Functional Equations in Banach Spaces”, Ukr. Math. J.  crossref  mathscinet  isi
    2. V. Yu. Slyusarchuk, “A criterion for the existence of almost periodic solutions of nonlinear differential equations with impulsive perturbation”, Ukrainian Math. J., 67:6 (2015), 948–959  crossref  mathscinet  zmath  isi  scopus
    3. 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
    4. 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
    5. V. E. Slyusarchuk, “Necessary and sufficient conditions for the existence and uniqueness of a bounded solution of the equation $\dfrac{dx(t)}{dt}=f(x(t)+h_1(t))+h_2(t)$”, Sb. Math., 208:2 (2017), 255–268  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    6. 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
    7. V. E. Slyusarchuk, “To Favard's theory for functional equations”, Siberian Math. J., 58:1 (2017), 159–168  mathnet  crossref  crossref  isi  elib  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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