Existence Results for Partial Neutral Functional Differential Equations with Unbounded Delay

Abstract

This work is concerned with a class of quasi-linear partial neutral functional differential equations with unbounded delay. Specifically, we establish existence of mild and strong solutions for equations that can be described as an abstract functional differential equationd/dt(x(t)+F(t,xt))=Ax(t)+G(t,xt), whereAis the infinitesimal generator of a strongly continuous semigroup of linear operators on a Banach space andFandGare appropriate functions defined on a phase space. © 1998 Academic Press.