Caratheodory perturbation of a second-order differential inclusion with constraints

Abstract

We prove the existence of local solutions for the second-order viability problem ẍ(t) ∈ ƒ(t,x(t), ẋ(t)) + F(x(t), ẋ(t)), x(t) ∈ K. Here K is a closed subset of ℝn, F is an upper semicontinuous multifunction with compact values contained in the subdifferential of a convex proper lower semicontinuous function V, and ƒ is a Carathéodory function.