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Erschienen in:
2008 | OriginalPaper | Buchkapitel
On Generalized Differential Quotients and Viability
verfasst von : Ewa Girejko, Zbigniew Bartosiewicz
Erschienen in: Differential Equations, Chaos and Variational Problems
Verlag: Birkhäuser Basel
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Differential inclusions with constraints of the form
$$ \dot y\left( t \right) \in F\left( {t,y\left( t \right)} \right),{\mathbf{ }}y\left( t \right) \in K\left( t \right). $$
and the viability problem for such inclusions are studied. It is assumed that
t
↠
K
(
t
) is a set-valued map that has a GDQ-regular multiselection and (
t, y
) ↠
F
(
t, y
) is a set-valued map measurable with respect to
t
and upper semi-continuous with respect to
y
. Some auxiliary results on Cellina continuously approximable multifunctions and Generalized Differential Quotients are given.