Global Existence for some Neutral Functional Integrodifferential Equations with Finite Delay

In this paper, we study a class of neutral partial functional integrodifferential equations with finite delay in Banach spaces. We are interested in the global existence, uniqueness and regularity of solutions with values in the subspace $D(A).$ The method used are based on Banach's fixed point theorem and on the technique of the graph norm. In our work the nonlinear term is treated as a perturbation of the linear equation. As an application, we consider a diffusive neutral partial functional integrodifferential equation.