Int. Journal of Math. Analysis, Vol. 2, 2008, no. 21, 1023 - 1029 A Remark on the Existence of Positive Solution to a Nonlinear Semipositone System Involving the Weight Function G. A. Afrouzi a , J. Vahidi a,b and S. H. Rasouli a a Department of Mathematics, Faculty of Basic Sciences Mazandaran University, Babolsar, Iran b Department of Computer Sciences Shomal University, Amol, Iran afrouzi@umz.ac.ir, j.vahidi@umz.ac.ir, s.h.rasouli@umz.ac.ir Abstract In this note we are mainly concerned with existence result for semi- linear semipositone elliptic equation of the form ⎧ ⎨ ⎩ -Δu = λa(x)v α - c, x ∈ Ω, -Δv = λb(x)u β - c, x ∈ Ω, u = v =0, x ∈ ∂ Ω, where Δ denote the Laplacian operator, Ω is a bounded domain in R N (N> 1) with ∂ Ω of class C 2 , λ, c are positive parameters, α, β > 0 and the weight a(x), b(x) satisfying a(x) ∈ C (Ω), b(x) ∈ C (Ω) and a(x) ≥ a 0 > 0, b(x) ≥ a 0 > 0 for x ∈ Ω. We prove the existence of positive solution via the method of sub-super solutions. Mathematics Subject Classification: 35J55 Keywords: Semipositone system; Positive solutions; Method of sub-super solutions