Multivalued second order differential problem

Ewelina Mainka-Niemczyk


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

D2(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.


set-valued sine and cosine families; Riemann integral for set-valued functions; Hukuhara derivative of a set-valued function

Mathematics Subject Classification

26E25; 47H04; 47D09; 39B52


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