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

• Date: 2016
• Main Authors: Slyusarchuk, V. Yu., Слюсарчук, В. Ю.
• Format: Article
• Language: Ukrainian
• Published: Institute of Mathematics, NAS of Ukraine 2016
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/1921
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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...