Nonlinear abstract differential equations with deviated argument

In this paper we consider the nonlinear differential equation with deviated argument u (t) = Au(t) + f (t,u(t),u[ϕ(u(t), t)]), t ∈ R+, in a Banach space (X, · ), where A is the infinitesimal generator of an analytic semigroup. Under suitable conditions on the functions f and ϕ, we prove a global existence and uniqueness result for the above equation. © 2006 Elsevier Inc. All rights reserved