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On a multivalued second order differential problem with Hukuhara derivative

Piszczek M.

Opuscula Mathematica

2008

Vol. 28, no. 2

151-161

Let K be a closed convex cone with the nonempty interior in a real Banach space and let cc(K) denote the family of all nonempty convex compact subsets of K. Assume that continuous linear multifunctions H, ψ : K → cc(K) are given. We consider the following problem D2 φ (t, x) = φ (t, H(x)), D φ (t,x) / (t=0) = {0}, φ (0, x) = ψ (x) for t ≥ 0 and x ∈ K, where D φ (t, x) denotes the Hukuhara derivative of φ (t, x) with respect to t.

On multivalued cosine families

Piszczek M.

Journal of Applied Analysis

2007

Vol. 13, nr 1

57-76

Let K be a convex cone in a real Banach space. The main purpose of this paper is to show that for a regular cosine family {F t : t ∈ R} of linear continuous multifuoctions Ft: K → cc(X) there exists a linear continuous multifunction H: K → cc(K) such that [wzór].