Smoothing of nonsmooth differential systems near regular-tangential singularities and boundary limit cycles

Abstract Understanding how tangential singularities evolve under smoothing processes was one of the first problem concerning regularization Filippov systems. In this paper, we are interested in C n -regularizations systems around visible regular-tangential even multiplicity. More specifically, using Fenichel theory and blow-up methods, aim to understand trajectories regularized system transits through region regularization. We apply our results investigate boundary limit cycles with multiplicity contact switching manifold.