Uniqueness and existence of positive solutions for some semilinear elliptic systems Original Research Article

We are concerned with the uniqueness and existence of positive solutions for the following Dirichlet problem: View the MathML source-Δui=∏j=1NujpijinΩ,ui=0on∂Ω,i=1,2,…,N, Turn MathJax on where ΩΩ is a bounded domain of class View the MathML sourceC2,α,α∈(0,1). We prove uniqueness and existence under the assumption that I-PI-P is a nonsingular irreducible MM-matrix, where II is the identity matrix and P=(pij)P=(pij) with View the MathML sourcepij⩾0(i,j=1,…,N).