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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
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