  This paper considers homogeneous order preserving continuous maps on the
normal cone of an ordered normed vector space. It is shown that certain
operators of that kind which are not necessarily compact themselves but have a
compact power have a positive eigenvector that is associated with the cone
spectral radius. We also derive conditions for the existence of homogeneous
order preserving eigenfunctionals. Our results are illustrated in a model for
spatially distributed two-sex populations.
