Geodesic
Necessary and sufficient conditions for the existence and uniqueness of a~bounded solution of the equation $\dfrac{dx(t)}{dt}=f(x(t)+h_1(t))+h_2(t)$
Sbornik. Mathematics, Tome 208 (2017) no. 2, pp. 255-268

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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. 
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     author = {V. E. Slyusarchuk},
     title = {Necessary and sufficient conditions for the existence and uniqueness of a~bounded solution of the equation $\dfrac{dx(t)}{dt}=f(x(t)+h_1(t))+h_2(t)$},
     journal = {Sbornik. Mathematics},
     pages = {255--268},
     publisher = {mathdoc},
     volume = {208},
     number = {2},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2017_208_2_a4/}
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V. E. Slyusarchuk. Necessary and sufficient conditions for the existence and uniqueness of a~bounded solution of the equation $\dfrac{dx(t)}{dt}=f(x(t)+h_1(t))+h_2(t)$. Sbornik. Mathematics, Tome 208 (2017) no. 2, pp. 255-268. http://geodesic.mathdoc.fr/item/SM_2017_208_2_a4/