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

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.
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