Attractors for Differential Equations with Variable Delays

The theory of global attractors for autonomous systems as developed by Hale in [7] owes much to examples arising in the study of retarded functional differential equations [8] (for slightly different approaches see Babin and Vishik [1], Ladyzhenskaya [13], or Temam [16]). Although the classical theory can be extended in a relatively straightforward manner to deal with time-periodic equations, general non-autonomous equations such as ẋ t = F t x t x t − ρ t (1) fall outside its scope. Recently, a theory of “pullback attractors” has been developed (see Section 2) which allows many of the ideas from the autonomous theory to