FUNCTIONAL DIFFERENTIAL EQUATIONS WITH UNBOUNDED DELAY IN EXTRAPOLATION SPACES

We study the existence, regularity and stability of solutions for nonlinear partial neutral functional differential equations with unbounded delay and a Hille-Yosida operator on a Banach space X. We consider two nonlinear perturbations: the first one is a function taking its values in X and the second one is a function belonging to a space larger than X, an extrapolated space. We use the extrapolation techniques to prove the existence and regularity of solutions and we establish a linearization principle for the stability of the equilibria of our equation.