Сірченко З. Ф.

Устанавливается теорема о непрерывной зависимости решений некоторых параболических граничных задач от параметра и, как следствие из этой теоремы, теорема об усреднении.

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.