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

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

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

Bibliographic databases:

UDC: 517.925.52
MSC: 34C27

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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• http://mi.mathnet.ru/eng/msb8188
• 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.
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
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
4. V. Yu. Slyusarchuk, “Necessary and sufficient conditions for the invertibility of nonlinear differentiable maps”, Ukrainian Math. J., 68:4 (2016), 638–652
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
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
7. V. E. Slyusarchuk, “To Favard's theory for functional equations”, Siberian Math. J., 58:1 (2017), 159–168
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