2019
Том 71
№ 11

# Sirchenko Z. F.

Articles: 3
Article (Ukrainian)

### On the application of the principle of averaging for the solution of some parabolic boundary value problems

Ukr. Mat. Zh. - 1973. - 25, № 5. - pp. 621—631

Article (Russian)

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

Ukr. Mat. Zh. - 1964. - 16, № 3. - pp. 339-350

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.

Brief Communications (Russian)

### Application of tre a veraging method to the solution of partial differential equations

Ukr. Mat. Zh. - 1962. - 14, № 2. - pp. 222-226