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.