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

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

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

Bibliographic databases:

UDC: 517.988.6
MSC: 34K12, 34K13

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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• http://mi.mathnet.ru/eng/msb7844
• https://doi.org/10.4213/sm7844
• http://mi.mathnet.ru/eng/msb/v203/i5/p135

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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.
2. J. Math. Sci. (N. Y.), 194:4 (2013), 440–452
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
4. J. Math. Sci. (N. Y.), 197:1 (2014), 122–128
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
6. V. E. Slyusarchuk, “Conditions for almost periodicity of bounded solutions of non-linear differential-difference equations”, Izv. Math., 78:6 (2014), 1232–1243
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
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
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
10. V. Yu. Slyusarchuk, “Necessary and sufficient conditions for the invertibility of nonlinear differentiable maps”, Ukrainian Math. J., 68:4 (2016), 638–652
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
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