2018
Том 70
№ 8

# Extension of a theorem of N. N. Bogoliubov to the case of a Hilbert space

Sirchenko Z. F.

Abstract

The author considers an equation in standard form $$\frac{dx}{dt} = \varepsilon X(t,x) \quad(1)$$ where $x(t), X(t,x)$ are vector functions with values in the Hilbert space $H \varepsilon$ is a small parameter. A theorem is proved on the existence and uniqueness of an almost periodic solution of equation (1) in the neighborhood of the equilibrium position of the corresponding averaged equation $$\frac{dx}{dt} = \varepsilon X_0(x) \quad(2)$$ The question oi the stability of this solution is also decided.

Citation Example: Sirchenko Z. F. Extension of a theorem of N. N. Bogoliubov to the case of a Hilbert space // Ukr. Mat. Zh. - 1964. - 16, № 3. - pp. 339-350.

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