Green–Samoilenko operator in the theory of invariant sets of nonlinear differential equations - Perestyuk, N. A.; Slyusarchuk, V. Yu. (Ukrains’kyi Matematychnyi Zhurnal, 2009)
We establish conditions for the existence of an invariant set of the system of differential equations dφdt = a(φ),dxdt = 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.