A Viability Result for Second-Order Differential Inclusions

Abstract

We prove a viability result for the second-order differential inclusion x'' ∈ F(x,x'), (x(0), x'(0)) = (x0, y0) ∈ Q := K x Ω, where K is a closed and Ω is an open subsets of ℝm, and is an upper semicontinuous set-valued map with compact values, such that F(x, y) ⊂ ∂V(y), for some convex proper lower semicontinuous function V.