Solutions of semilinear elliptic equations in R-N with conical-shaped level sets

This article deals with the questions of the existence, of the uniqueness a nd of the qualitative properties of solutions of semilinear elliptic equati ons in R-N Three types of conical conditions at infinity are successively c onsidered. This defines three frameworks: the weak framework, the strong fr amework and the framework of solutions with asymptots. The results are base d on different kinds of sliding methods and, following the ideas of Beresty cki, Nirenberg and Vega, on comparison principles in cones or in R-N.