Abstract
We prove some existence of positive solutions to the semilinear elliptic system
Delta u = lambda p(x)g(v) Delta v = mu g(x)f(u)
in the half space R-+(n), n >= 2, subject to some Dirichlet conditions, where lambda and mu are nonnegative parameters. The functions f, g are nonnegative continuous monotone on (0, infinity) and the potentials p, q are nonnegative and satisfy some hypotheses related to the Kato class K-infinity(R-+(n)).