Existence and stability for some partial neutral functional differential equations

Abstract

In this work we study the existence and stability for some neutral partial functional differential equations. We suppose that the linear part is not necessarily densely defined and satisfies the Hille-Yosida condition on a Banach space $X$. The nonlinear term takes its values in a space larger than $X$, namely the extrapolated Favard class corresponding to the extrapolated semigroup corresponding to the linear part. Our approach is based on the theory of the extrapolation spaces.