Existence Results for Partial Neutral Functional Differential Equations with Unbounded Delay

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 equation drdt x t.qF t, xt..sAx t.qG t, xt., where A is the infinitesimal generator of a strongly continuous semigroup of linear operators on a Banach space and F and G are appropriate functions defined on a phase space