© 2017 Elsevier B.V. This work is devoted to study the existence of periodic solutions for a class of ε-family of discontinuous differential systems with many zones. We show that the averaged functions at any order control the existence of crossing limit cycles for systems in this class. We also provide some examples dealing with nonsmooth perturbations of nonlinear centers.
- Averaging method
- Nonsmooth differential system
- Periodic solution
- Piecewise smooth differential system