Viability for Differential Inclusions on Graphs
Tóm tắt
Let X be a Banach space, I a nonempty, bounded interval and let
$K:I\leadsto X$
be a given multi-valued function. We rephrase the concept of tangent set introduced by Cârjă et al. (Trans Amer Math Soc, 2008; Viability, Invariance and Applications. North-Holland Mathematics Studies, vol. 207. Elsevier, 2007) by saying that a bounded set
$E\subseteq X$
is right tangent to
at
if
$\liminf_{h\downarrow0}{1}/{h}\,\text{\rm dist}(\xi+hE;K(\tau+h))=0$
. Next, by using a tangency condition expressed in the terms of this concept, we establish several necessary and sufficient conditions for viability referring to differential inclusions on graphs.
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