Une méthode des sur et sous solutions améliorée

The usual upper and lower solutions method for solving a second order nonlinear elliptic equation is iterative, with the drawback of a tricky, if not sometimes impossible, derivation of the (quite essential) uniform C2 estimate, due to the occurence in the same equation of two successive iteration unknowns. We present here a method free of such a drawback, based on an elementary fixed point argument. To cite this article: P. Delanoë, C. R. Acad. Sci. Paris, Ser. I 341 (2005).