This paper is concerned with the lower semicontinuity of attractors for semilinear\udnon-autonomous differential equations in Banach spaces. We require the unperturbed\udattractor to be given as the union of unstable manifolds of time-dependent hyperbolic\udsolutions, generalizing previous results valid only for gradient-like systems in which\udthe hyperbolic solutions are equilibria. The tools employed are a study of the continuity\udof the local unstable manifolds of the hyperbolic solutions and results on the continuity of\udthe exponential dichotomy of the linearization around each of these solutions.
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