## The averaging principle on the semi-axis for dissipative systems.(Russian)Zbl 0658.34038

The paper under review provides the justification of the averaging method on $$R^+$$ for dissipative systems of the form (1) $$dx/dt=\epsilon g(t,x)$$ where $$g\in H(f)$$, the hull of an $$f\in C(R\times R^ n,R^ n)$$. Sufficient conditions on f ensuring the dissipativity of (1) (for all $$g\in H(f)$$, $$\epsilon \in (0,\epsilon_ 0))$$ are given. The existence of solutions with various recurrence properties is also investigated.
Reviewer: P.Moson

### MSC:

 34C29 Averaging method for ordinary differential equations

### Keywords:

recurrence properties
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