Second Order Viability Problems for Differential Inclusions

This paper gives necessary and sufficient conditions ensuring the existence of a solution to the second order differential inclusion x″(t) ∈ F(x(t), x′(t)), x(0) = x0, x′(0) = v0 such that x(t) ∈ K where K is a nonempty given subset of Rn. Furthermore, second order interior tangent sets are introduced and studied to obtain such conditions