Systèmes de réaction-diffusion sans propriété de Fredholm

We are interested in semi-linear elliptic systems in an infinite cylinder in the case where the components of the nonlinearity vector are linearly dependent. Such systems arise in particular in combustion theory. They do not satisfy the Fredholm property, and the conventional methods of nonlinear analysis are not applicable. The aim of this work is to develop new methods of analysis to study these problems. They are based on the introduction of integro-differential equations for which we prove the Fredholm property and construct the topological degree. These tools are applied to study existence of travelling waves and bifurcations of solutions. To cite this article: A. Ducrot et al., C. R. Acad. Sci. Paris, Ser. I 340 (2005).