Conditions of existence of bounded and almost periodic solutions of nonlinear differential equation with perturbations of solutions - Slyusarchuk, V. Yu. (Ukrains’kyi Matematychnyi Zhurnal, 2016)
We present the conditions of existence and uniqueness of bounded solutions of a nonlinear scalar differential equation$dx(t)/dt=f(x(t)+h(t)),\; t \in R$, in the case where a function $f$ is continuous on $R$ and a function $h$ is bounded and continuous. In addition, we study the case of an almost periodic function $h$.