Contribution to the study of some differential and functional systems.

Summary This work consists of two independent parts which consist in solving nonlinear functional differential systems. The first part concerns a dynamic equilibrium problem in a framework of incomplete markets. It highlights the appearance of macroeconomic fluctuations due to the incompleteness of the economy. It is devoted to the resolution of differential systems whose solutions provide an equilibrium for the economic model studied. The search for these solutions comes down to the search for fixed points for increasing applications or fixed points for applications on firm convexes. It requires very technical and specific constructions of the problem in question. The second part concerns an elliptic problem with mixed boundary conditions of the Dirichlet Neumann type, which originates from a model for semiconductors. We study the existence and regularity of a solution of this problem using the leray-schauder degree theory.