Abstract
This paper deals with the existence and the asymptotic behavior of positive continuous solutions of the nonlinear elliptic system Delta u = p(x) u(alpha) v(gamma), Delta v = q (x) u(s) v(beta) in the half space R-+(n) : = {x = ( x(1)..., x(n)) is an element of R-n : x(n) > 0 }, n >= 2, where alpha,beta >= 1 and r; s >= 0. The functions p and q are required to satisfy some appropriate conditions related to the Kato class K-infinity (R-+(n)). Our approach is based on potential theory tools and the use of Schauder's fixed point theorem.