On the existence of solutions for functional differential inclusions in Banach spaces (Q1184868)

Using some compactness arguments the authors prove a local (global) existence result concerning a class of functional differential inclusions of the form \(\dot x(t)\in G(t,x_ t)\), \(t\in[0,T]\), \(x(s)=\varphi^ 0(s)\), \(s\in[-h,0]\). Here \(E\) is a real separable Banach space, \(D\) is an open subset in \(C_ E[-h,0]\) and \(G: [0,T]\times G\to 2^ E\) is a convex-closed valued measurable and upper semicontinuous function with respect to the weak topology on \(E\).