PERIODIC SOLUTIONS FOR SINGULARLY PERTURBED SYSTEMS IN INFINITE DIMENSIONAL SPACES WITH HYSTERESIS: AN AVERAGING APPROACH
Anastasie Gudovich, Mikhail Kamenskiĭ, Paolo Nistri · Use Siena air (University of Siena) · 2004
We consider a singularly perturbed system of two semilinear parabolic equations with nonlinear high frequency inputs which contain the output of a Krasnosel'skii-Pokrovskii hysteresis operator. For sufficiently small values of the perturbation parameter > 0, we show the existence of periodic solutions, and we describe their behaviour as ! 0. The employed approach is based on an averaging method together with topological degree arguments.