Contributions to mathematical analysis of non-linear models with applications in population dynamics

Résumé

The PhD thesis deals with two research lines, both within the framework of mathematical analysis of non-linear models. The main differences appear in the type of equations we consider and the approach used. On the one hand, we give some extensions of fixed point results that improve the localization of solutions to boundary or initial value problems and we contribute to the application of fixed point theory to population models. On the other hand, our main aim is to describe the asymptotic dynamics and bifurcations of some discrete-time one-dimensional dynamical systems. We follow a more applied-oriented approach, dealing with some population models arising in fisheries management or blood cell production.