Abstract

We generalize the Lyapunov-Schmidt reduction for the case of nonsmooth finite dimensional functions. By means of this generalization we prove the existence of T-periodic solutions for nonlinear differential systems coming from a nonsmooth T-periodic perturbation of a family of T-periodic solutions. When the perturbation is smooth our result coincides with the classical result of Malkin. An example illustrating the main result is also provided. This is a joint work with Jaume Llibre and Oleg Makarenkov.