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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.

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
Full Text: DOI
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