Chaos in a Periodically Perturbed Second-Order Equation with Signum Nonlinearity

We study the periodically perturbed Duffing-type equation g(x) = e(t) and its damped counterpart + g(x) = e(t). The main feature of our model is the presence of a "signum term" in g(x). We prove the existence of infinitely many subharmonic solutions as well as the presence of chaotic dynamics for some T-periodic forcing terms.