2017
Том 69
№ 7

# Conditions of existence of bounded and almost periodic solutions of nonlinear differential equation with perturbations of solutions

Slyusarchuk V. Yu.

Abstract

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 $h$.

Citation Example: Slyusarchuk V. Yu. Conditions of existence of bounded and almost periodic solutions of nonlinear differential equation with perturbations of solutions // Ukr. Mat. Zh. - 2016. - 68, № 9. - pp. 1286-1296.