Differential inclusions on closed sets in Banach spaces with application to sweeping process

Houcine Benabdellah

DOI: http://dx.doi.org/10.12775/TMNA.2004.006

Abstract


This paper deals with the existence of absolutely continuous solutions of a
differential inclusion with state constraint in a separable Banach space%
$$
x( 0) =x_{0}, \quad x( t) \in C( t) ,\quad
\dot{x}( t) \in F( t,x( t) )
$$
where $C\colon [ 0,a] \rightarrow X$ is a multifunction with closed graph
$G$ and $F\colon G\rightarrow X$ is a convex compact valued multifunction
which is
separately measurable in $t\in[ 0,a] $ and separately upper
semicontinuous in $x\in X$. Application to a non convex sweeping process is
also considered.

Keywords


Differential inclusions; Bouligand cone; Scorza-Dragoni theorem

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