Existence of positive bounded solutions for some nonlinear elliptic systems

We prove some existence results of positive bounded continuous solutions to the semilinear elliptic system Δ u = λ p ( x ) g ( v ) , Δ v = μ q ( x ) f ( u ) in domains D with compact boundary subject to some Dirichlet conditions, where λ and μ are nonnegative parameters. The functions f , g are nonnegative continuous monotone on ( 0 , ∞ ) and the potentials p, q are nonnegative and satisfy some hypotheses related to the Kato class K ( D ) .