Global attractivity in concave or sublinear monotone infinite delay differential equations,

with Rafael Obaya and Ana M. Sanz,
J. Differential Equations 246 (8) (2009), 3332-3360.

The dynamical behavior of the trajectories defined by a recurrent family of monotone

functional differential equations with infinite delay and concave or sublinear nonlinearities is

studied. Different sceneries which require the existence of a lower solution and of a bounded trajectory

ordered in an appropriate way are analyzed: the existence of a globally asymptotically stable

minimal set given by a 1-cover of the base flow is proved. These results are applied to the

description of the long term dynamics of a nonautonomous model representing a stage-structured

population growth without irreducibility assumptions on the coefficient matrices.