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Mat. Sb., 2017, Volume 208, Number 2, Pages 88–103 (Mi msb8684)  

Necessary and sufficient conditions for the existence and uniqueness of a bounded solution of the equation $\dfrac{dx(t)}{dt}=f(x(t)+h_1(t))+h_2(t)$

V. E. Slyusarchuk

Ukranian State Academy of Water Economy, Rivne, Ukraine

Abstract: Necessary and sufficient conditions for a bounded solution of the nonlinear scalar differential equation $dx(t)/dt=f(x(t)+h_1(t))+h_2(t)$, $t\in\mathbb{R}$, to exist and be unique are presented in the case when $f(x)$ is a continuous function and the functions $h_1(t)$ and $h_2(t)$ are bounded and continuous. The case when $h_1(t)$ and $h_2(t)$ are almost periodic functions is also investigated.
Bibliography: 31 titles.

Keywords: nonlinear differential equations, bounded and almost periodic solutions.

DOI: https://doi.org/10.4213/sm8684

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English version:
Sbornik: Mathematics, 2017, 208:2, 255–268

Bibliographic databases:

Document Type: Article
UDC: 517.988.63
MSC: 34A34, 34C11, 34C27
Received: 26.02.2016

Citation: V. E. Slyusarchuk, “Necessary and sufficient conditions for the existence and uniqueness of a bounded solution of the equation $\dfrac{dx(t)}{dt}=f(x(t)+h_1(t))+h_2(t)$”, Mat. Sb., 208:2 (2017), 88–103; Sb. Math., 208:2 (2017), 255–268

Citation in format AMSBIB
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