An Existence Result on Positive Solutions for a Quasilinear Reaction-Diffusion System

We consider the existence of positive solutions for the reactiondiffusion system where λ is a positive parameter, Δ is the Laplacian operator, β₁, γ₂, α₃ > 0, α₁, α₂, β₂, β₃, γ₁, γ₃ ≥ 0, and Ω is a bounded domain in R^N (N > 1) with smooth boundary ∂Ω.We prove the existence of positive solution for each λ > 0. We establish our results by using the method of subsuper solutions.