On a Nonlinear System of Reaction-Diffusion Equations - Afrouzi, G. A.; Rasouli, S. H. (Nonlinear Analysis: Modelling and Control, 2006)
The aim of this article is to study the existence of positive weak solution for a quasilinear reaction-diffusion system with Dirichlet boundary conditions,− div(|∇u1|p1−2∇u1) = λu1α11u2α12... unα1n,   x ∈ Ω,− div(|∇u2|p2−2∇u2) = λu1α21u2α22... unα2n,   x ∈ Ω, ... , − div(|∇un|pn−2∇un) = λu1αn1u2αn2... unαnn,   x ∈ Ω,ui = 0,   x ∈ ∂Ω,   i = 1, 2, ..., n, where λ is a positive parameter, Ω is a bounded domain in RN (N > 1) with smooth boundary ∂Ω. In addition, we assume that 1
Keywords: s: reaction-diffusion system; p-Laplacian; positive weak solutions