Periodic averaging theorems for various types of equations (Q655492)

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.