Extrapolation Spaces and Partial Neutral Functional Differential Equations with infinite delay
Abstract
We study the existence regularity and stability of solutions for some nonlinear partial neutral functional differential equations with infinite delay. In our system, the unbounded linear term is a Hille-Yosida operator on a Banach space, and the nonlinear function takes its values on some spaces larger than the initial Banach space, namely the extrapolated Favard class corresponding to the semigroup generated by the unbounded linear operator. We give also a linearized stability principle to study the behavior of solutions near the equilibriums of the model.