2018
Том 70
№ 6

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

Abstract

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.

English version (Springer): Ukrainian Mathematical Journal 61 (2009), no. 7, pp 1123-1136.

Citation Example: Perestyuk N. A., Slyusarchuk V. Yu. Green–Samoilenko operator in the theory of invariant sets of nonlinear differential equations // Ukr. Mat. Zh. - 2009. - 61, № 7. - pp. 948-957.

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