Existence in the large for nonlinear delay evolution inclusions with nonlocal initial conditions

In this paper we provide a sufficient condition for the existence of C0C0-solutions for a class of nonlinear functional differential evolution equation of the form{u′(t)∈Au(t)+f(t),t∈R+,f(t)∈F(t,u(t),ut),t∈R+,u(t)=g(u)(t),t∈[−τ,0], where X is a real Banach space, A   is the infinitesimal generator of a nonlinear compact semigroup, F:R+×X×C([−τ,0];D(A)¯)⇝X is a nonempty convex and weakly compact valued multi-function and g:Cb([−τ,+∞);D(A)¯)→C([−τ,0];D(A)¯).