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

with Rafael Obaya, Sylvia Novo and Ana M. Sanz,
Discrete Cont. Dyn. Sys. - Ser. A, to appear.

A detailed dynamical study of the skew-product semiflows induced by families of AFDEs with infinite delay

on a Banach space is carried over. Applications are given for families of non-autonomous quasimonotone

reaction-diffusion PFDEs with delay in the nonlinear reaction terms, both with finite and infinite delay. In this

monotone setting, relations among the classical concepts of sub and super solutions and the dynamical

concept of semi-equilibria are established, and some results on the existence of minimal semiflows with

a particular dynamical structure are derived.


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