A Remark on the Existence of Positive Solution to a Nonlinear Semipositone System Involving the Weight Function

In this note we are mainly concerned with existence result for semilinear semipositone elliptic equation of the form ⎧⎨ ⎩ −Δu = λa(x)vα − c, x ∈ Ω, −Δv = λb(x)uβ − c, x ∈ Ω, u = v = 0, x ∈ ∂Ω, where Δ denote the Laplacian operator, Ω is a bounded domain in RN (N > 1) with ∂Ω of class C2, 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) ≥ a0 > 0, b(x) ≥ a0 > 0 for x ∈ Ω. We prove the existence of positive solution via the method of sub-super solutions. Mathematics Subject Classification: 35J55