On semicoercive sweeping process with velocity constraint

In this note, by solving a variational inequality at each iteration, we study the existence of solutions for a class of sweeping processes with velocity in the moving set, originally introduced in a recent paper (Adly et al. in Math Program Ser B 148(1):5–47, 2014). Our aim is to improve Adly et al. (2014, Theorem 5.1) to allow possibly unbounded moving sets. The theoretical result is supported by some examples in nonregular electrical circuits.