Abstract
We prove some existence results of positive bounded continuous solutions to the semilinear elliptic system Delta u = lambda p(x)g(v), Delta v = mu q(x)f(u) in domains D with compact boundary 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(D). (C) 2008 Elsevier Inc. All rights reserved.