In this work we investigate some asymptotic properties of an age-structured
Lotka-Volterra model, where a specific choice of the functional parameters
allows us to formulate it as a delayed problem, for which we prove the
existence of a unique coexistence equilibrium and characterize the existence of
a periodic solution. We also exhibit a Lyapunov functional that enables us to
reduce the attractive set to either the nontrivial equilibrium or to a periodic
solution. We then prove the asymptotic stability of the nontrivial equilibrium
where, depending on the existence of the periodic trajectory, we make explicit
the basin of attraction of the equilibrium. Finally, we prove that these
results can be extended to the initial PDE problem.Comment: 29 page