On A Second-Order Differential Inclusion With Constraints∗

We prove the existence of viable solutions to the Cauchy problem x′ ′ ∈ F (x,x′) + f(t, x, x′), x(0) = x0, x′(0) = y0, x(t) ∈ K, where K ⊂ Rn is a closed set, F is a set-valued map contained in the Fréchet subdifferential of a φ- convex function of order two and f is a Carathéodory map.