Skew-product semiflows for non-autonomous partial functional differential equations with delay

Abstract

A detailed dynamical study of the skew-product semiflows induced byfamilies of AFDEs with infinite delay on a Banach space iscarried over. Applications are given for families of non-autonomousquasimonotone reaction-diffusion PFDEs with delay in the nonlinearreaction terms, both with finite and infinite delay. In thismonotone setting, relations among the classical concepts of sub andsuper solutions and the dynamical concept of semi-equilibria areestablished, and some results on the existence of minimal semiflowswith a particular dynamical structure are derived.