Green–Samoilenko operator in the theory of invariant sets of nonlinear differential equations

• Date: 2009
• Main Authors: Perestyuk, N. A., Slyusarchuk, V. Yu., Перестюк, М. О., Слюсарчук, В. Ю.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 2009
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3069
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We establish conditions for the existence of an invariant set of the system of differential equations $$\frac{dφ}{dt} = a(φ),\quad \frac{dx}{dt} = P(φ)x + F(φ,x),$$ where $a: Φ → Φ, P: Φ → L(X, X)$, and $F: Φ × X→X$ are continuous mappings and $Φ$ and $X$ are finite-dimensional Banach spaces....