Periodic Solutions for Non-linear Equations of Structured Populations

We show the existence of non-trivial periodic solutions for a class of non-linear equations, model of age-structured populations. To this aim we use the theory of Centre Manifold for a class of abstract differential equations introduced by Desch and Schappacher, and show that a Hopf Bifurcation Theorem can be proved for this class of equations. Finally, we consider some special cases, and present an algorithm for the determination of the type of bifurcation, and show that in the considered cases the bifurcation is always supercritical