Perturbing semigroups by solving Stieltjes renewal equations

We develop a perturbation theory for strongly continuous semigroups and dual semigroups not based on perturbation of infinitesimal generators but on certain families of bounded linear operators describing the cumulative effect of the feedback. The theory extends the theory of perturbation of generators by bounded or relatively bounded linear operators. The theory is applied to problems of structured population dynamics which cannot, to the best of our knowledge, be treated using a more conventional perturbation theory.