Abstract. In this paper we deal with nonlinear differential systems of the formwherefunctions, T -periodic in the first variable, being D an open subset of R n , and ε a small parameter. For such differential systems, which do not need to be of class C 1 , under convenient assumptions we extend the averaging theory for computing their periodic solutions to k-th order in ε. Some applications are also performed.

The main objective of this work is to develop, via Brower degree theory and regularization theory, a variation of the classical averaging method for detecting limit cycles of certain piecewise continuous dynamical systems. In fact, overall results are presented to ensure the existence of limit cycles of such systems. These results may represent new insights in averaging, in particular its relation with non smooth dynamical systems theory. An application is presented in careful detail

No abstract