Averaging of time-varying differential equations revisited.

*(English)*Zbl 1135.34031The author is throwing a new look at the method of averaging for ordinary differential equations, as described e.g. in the book “Averaging methods in nonlinear dynamical systems” [New York etc.: Springer-Verlag (1985; Zbl 0586.34040) (2nd ed. 2007; Zbl 1128.34001)] by J. A. Sanders and F. Verhulst. First, wellknown results of this theory are rederived by a new method that allows weaker conditions than the usual ones. Then, a rather complicated counterexample of a differential equation is constructed showing that a statement in the above-mentioned book (Theorem 3.4.5) is erroneous. Finally, the author uses his method to prove some generalizations and extensions of known results by weakening the standard assumptions, and, moreover, by applying it to delay differential equations.

Reviewer: Josef Hainzl (Freiburg)

##### MSC:

34C29 | Averaging method for ordinary differential equations |

##### Keywords:

averaging
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\textit{Z. Artstein}, J. Differ. Equations 243, No. 2, 146--167 (2007; Zbl 1135.34031)

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##### References:

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