In this paper we deal with nonlinear differential systems of the form x'(t) = Σki=0 εiFi (t, x) + εk+1R(t, x, ε), where Fi : R × D → Rn for i = 0, 1, . . . , k, and R : R×D×(- ε0, ε0) → Rn are continuous functions, and T -periodic in the first variable, D being an open subset of Rn, and ε a small parameter. For such differential systems, which do not need to be of class C1, under convenient assumptions we extend the averaging theory for computing their periodic solutions to k-th order in ε. Some applications are also performed. © 2014 IOP Publishing Ltd.
- Brouwer degree
- averaging method
- discontinuous differential system
- non-smooth differential system
- periodic solution