A viability result for Carath�odory non-convex differential inclusion in Banach spaces

This paper deals with the existence of solutions to the following differential inclusion: \(\dot{x}(t)\in F(t,x(t))\) a.e. on \([0, T[\) and \(x(t)\in K\), for all \(t \in [0, T]\), where \(F: [0, T]\times K \rightarrow 2^E\) is a Carath�odory multifunction and \(K\) is a closed subset of a separable Banach space \(E\).