This article is cited in 2 papers

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.

UDC: 517.988.63

MSC: 34A34, 34C11, 34C27

Received: 26.02.2016

DOI: 10.4213/sm8684

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

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