Averaging For Two Classes Of Non-autonomous Ordinary Differential Equations

In this paper, by helping the theories of Kurzweil integral and generalized ordi-nary differential equations, impulsive retarded functional differential equations and a class of discontinuous systems are equivalent to the generalized ordinary differential equations. Both periodic and non-periodic averaging theorem for impulsive retarded functional differential equations are established by using the averaging theorem for generalized ordinary differential equations. Further, both periodic and non-periodic averaging theorem for a class of discontinuous systems are established.