Mathematical Sciences: Boundary Layer Phenomena for Nonlinear Functional Differential Equations

This project will study differential delay equations and iterations of nonexpansive maps. Main emphasis will be placed in extending current knowledge to the cases of several delays and of delays depending on the state. In particular, for equations depending on a small parameter and delays depending on the state, the project will study the boundary layer phenomenon resulting in periodic solutions when the parameter tends to zero. Analysis of nonexpansive mappings through generalizations of properties of linear stochastic matrices will be pursued. Models in biology, economics, physics and even other branches of mathematics motivate the main problems to be studied. The generality of the questions will make the results relevant to most areas of basic science.