EXISTENCE AND STABILITY IN THE alpha-NORM FOR SOME PARTIAL FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAY

In this work, we discuss the existence, regularity and stability of solutions for some partial functional differential equations with infinite delay. We assume that the linear part generates an analytic semigroup on a Banach space X and the nonlinear part is a Lipschitz continuous function with respect to the fractional power norm of the linear part.