In this paper we consider differential 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.