Opuscula Mathematica

Opuscula Math.
, no. 2
 (), 151-161
Opuscula Mathematica

On a multivalued second order differential problem with Hukuhara derivative

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.
Mathematics Subject Classification: 26E25, 39B52, 47D09.
Cite this article as:
Magdalena Piszczek, On a multivalued second order differential problem with Hukuhara derivative, Opuscula Math. 28, no. 2 (2008), 151-161
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ISSN 1232−9274, e-ISSN 2300−6919, DOI https://doi.org/10.7494/OpMath
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