@Article{Piszczek2008,
author = "Piszczek, Magdalena",
title = "On a multivalued second order differential problem with Hukuhara derivative",
journal = "Opuscula Math.",
year = "2008",
volume = "28",
number = "2",
pages = "151--161",
doi = "http://dx.doi.org/10.7494/OpMath.2008.28.2.151",
url = "http://dx.doi.org/10.7494/OpMath.2008.28.2.151",
abstract = "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 \(H,\Psi : K \to cc(K)\) are given. We consider the following problem \[\begin{aligned}D^2\Phi(t,x) =& \Phi(t,H(x)),\\ D\Phi(t,x)|_{t=0} =& \{0\},\\ \Phi(0,x) =& \Psi(x)\end{aligned}\] for \(t \geq 0\) and \(x \in K\), where \(D\Phi(t,x)\) denotes the Hukuhara derivative of \(\Phi(t,x)\) with respect to \(t\).",
keywords = "Hukuhara's derivative, multivalued cosine families, Riemann integral for multifunctions, Cauchy problem for a set-valued differential equation",
issn = "1232-9274"
}