EXISTENCE AND STABILITY FOR SOME PARTIAL FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAY

We study the existence, regularity, and stability of solutions for some partial functional differential equations with infinite delay. We assume 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 space larger than X, namely the extrapolated Favard class of the extrapolated semigroup corresponding to the linear part. Our approach is based on the theory of the extrapolation spaces.