Some semilinear elliptic systems without variational structure

This work is motivated by the study of the following semilinear elliptic system, proposed by Gierer and Meinhardt as a model of morphogenesis, (UNFORMATTED TABLE OR EQUATION FOLLOWS);Chapter I of this thesis is devoted to the study of a priori estimates for the solution sets of (1)-(4) and other related systems, as well as to applications of these estimates to the problems of existence and nonexistence of nonconstant solutions.;In Chapter II, we consider (1)-(4) under radial symmetry assumptions. We focus here on the construction of a special family of solutions to (1)-(4) indexed by the parameter d, and exhibiting an internal layer as d approaches zero.