Abstract
In this paper we consider differential inclusions driven by a maximal monotone operator. First we show that for the nonconvex system the solution set viewed as a multifunction of the initial condition admits a continuous selector passing from a prescribed point. Then we use this selector to show the path connectedness of the solution set. We also investigate the continuity properties of the solution multifunction. Finally we solve a viability problem and we also establish the existence of periodic trajectories.