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.