Existence of solutions for second-order differential inclusions involving proximal normal cones

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 the solution is required to satisfy an impact law, appearing in the description of mechanical systems with inelastic shocks. (C) 2012 Elsevier Masson SAS. All rights reserved.