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

• Datum: 2016
• Hauptverfasser: Slyusarchuk, V. Yu., Слюсарчук, В. Ю.
• Format: Artikel
• Sprache: Ukrainisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2016
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/1921
• Назва журналу: 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...