On the birth of limit cycles for non-smooth dynamical systems
  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. 
Jaume Llibre, Douglas Duarte Novaes, Marco Antonio Teixeira
math.DS