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Periodic averaging theorems for various types of equations. (English) Zbl 1243.34060
The authors prove a periodic averaging theorem for generalized ordinary differential equations of the form \[ x'(t) = \epsilon f(t,x(t)) + \epsilon^2 g(t,x(t),\epsilon), \quad x(t_0) = x_0. \] They show that that this theorem implies other averaging theorems for ordinary differential equations with impulses or dynamic equations on time scales of analogous types. In a final section another periodic averaging theorem for retarded equations is shown.

MSC:
34C29 Averaging method for ordinary differential equations
34N05 Dynamic equations on time scales or measure chains
34A37 Ordinary differential equations with impulses
34K33 Averaging for functional-differential equations
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