TY  - JOUR
ID  - Piszczek2008
LB  - Piszczek2008
AU  - Piszczek, Magdalena
TI  - On a multivalued second order differential problem with Hukuhara derivative
ST  - On a multivalued second order differential problem with Hukuhara derivative
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2008
VL  - 28
IS  - 2
SP  - 151
EP  - 161
DO  - http://dx.doi.org/10.7494/OpMath.2008.28.2.151
UR  - http://dx.doi.org/10.7494/OpMath.2008.28.2.151
AB  - 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 \(t\).
KW  - Hukuhara's derivative
KW  - multivalued cosine families
KW  - Riemann integral for multifunctions
KW  - Cauchy problem for a set-valued differential equation
SN  - 1232-9274
ER  -