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 C-0-solutions for a class of nonlinear functional differential evolution equation of the form {u'(t) is an element of Au(t) + f(t), t is an element of R+, f(t) is an element of F(t, u(t), u(t)), t is an element of R+, u(t) = g(u)(t), t is an element of [-tau, 0], where X is a real Banach space, A is the infinitesimal generator of a nonlinear compact semigroup, F : R+ x X x C([-tau, 0]; <(D(A))over bar>) -> X is a nonempty convex and weakly compact valued multi-function and g : C-b([-tau, +infinity); <(D(A))over bar>) -> C([-tau, 0]; <(D(A))over bar>). (C) 2011 Elsevier Inc. All rights reserved.