  The paper focuses on positive solutions to a coupled system of parabolic
equations with nonlocal initial conditions. Such equations arise as
steady-state equations in an age-structured predator-prey model with diffusion.
By using global bifurcation techniques, we describe the structure of the set of
positive solutions with respect to two parameters measuring the intensities of
the fertility of the species. In particular, we establish co-existence
steady-states, i.e. solutions which are nonnegative and nontrivial in both
components.
