Bifurcations from nondegenerate families of periodic solutions in Lipschitz systems (Q765957)

The authors study periodic solutions of a perturbed ODE of the form \(x'=f(t,x)+\epsilon g(t,x,\epsilon)\), where the perturbation \(g\) and the smooth vector field \(f\) are T-periodic, and \(g\) is only locally uniformly Lipschitz with respect to its second variable. It is assumed that the unperturbed ODE has a nondegenerate family of T-periodic solutions. In this setting, the authors prove the existence of an isolated branch of T-periodic solutions of the perturbed system bifurcating from the solutions of the unperturbed ODE. For showing this, they study the zeroes of the so-called Malkin bifurcation function. The general approach is based on the Lyapunov-Schmidt reduction extended to the case of nonsmooth Lipschitz functions.