Multivalued second order differential problem
Abstract
Let K be a closed convex cone with nonempty interior in a real Banach space and let F, G, H: K →cc(K) be three given continuous additive set-valued functions. We study the existence and uniqueness of a solution of the second order differential problem D2Φ(t, x) = Φ(t, H(x)), Φ(0, x) = F(x), DΦ(t, x)|t=0 = G(x) for t ≥0 and x ∈K, where DΦ(t, x) and D2Φ(t, x) denote the Hukuhara derivative and the second Hukuhara derivative of Φ(t, x) with respect to t.
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