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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, 34 (10) (2014), 4291-4321.

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A detailed dynamical study of the skew-product semiflows induced by families

of abstract functional differential equations with infinite delay on a Banach

space is carried over. Applications are given for families of non-autonomous

quasimonotone reaction-diffusion equations 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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