Partial Functional Evolution Inclusions with Finite Delay

Abstract

In this chapter, we provide sufficient conditions for the existence of mild solutions on the semi-infinite interval \(J = \mathbb{R}_{+}\) for some classes of first order partial functional and neutral functional differential evolution inclusions with finite delay by using the recent nonlinear alternative of Frigon [114, 115] for contractive multi-valued maps in Frechet spaces [116], combined with the semigroup theory [16, 20, 168].