Existence of nonnegative solutions for a class of semilinear elliptic systems with indefinite weight

We prove the existence of nonnegative solutions to the system −Δu=λa(x)f(v)in Ω,−Δv=λb(x)g(u)in Ω,u=0=von ∂Ω, where ΩΩ is a bounded domain in RNRN with a smooth boundary ∂Ω,λ∂Ω,λ is a positive parameter. By the method of monotone iteration and Schauder fixed point theorem, we prove the existence of a nonnegative solution to the above system for λλ sufficiently small. In this study, we do not restrict the sign of aa and bb.