  In this work, we prove global existence of solutions for second order
differential problems in a general framework. More precisely, we consider
second order differential inclusions involving proximal normal cone to a
set-valued map. This set-valued map is supposed to take admissible values (so
in particular uniformly prox-regular values, which may be non-smooth and
non-convex). Moreover we require the solution to satisfy an impact law,
appearing in the description of mechanical systems with inelastic shocks.
