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 C0-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)). © 2011 Elsevier Inc. All rights reserved.