  In this work we establish conditions which guarantee the existence of
(strictly) positive steady states of a nonlinear structured population model.
In our framework the steady state formulation amounts to recasting the
nonlinear problem as a family of eigenvalue problems combined with a fixed
point problem. Amongst other things our formulation requires us to control the
growth behaviour of the spectral bound of a family of linear operators along
positive rays. For the specific class of model we consider here, this presents
a considerable challenge. We are going to show that the spectral bound of the
family of operators, arising from the steady state formulation, can be
controlled by perturbations in the domain of the generators (only). These new
boundary perturbation results are particularly important for models exhibiting
fertility controlled dynamics. As an important by-product of the application of
the boundary perturbation results we employ here we recover (using a recent
theorem by H.R. Thieme) the familiar net reproduction number (or function) for
models with single state at birth, which include for example the classic
McKendrick (linear) and Gurtin-McCamy (non-linear) age-structured models.
