Uniqueness and existence of positive solutions for some semilinear elliptic systems

摘要

We are concrned with the uniqueness and existence of positive solutions for the following Dirichlet problem:[GRAPHICS]where Omega is a bounded domain of class C-2,C-alpha, alpha epsilon (0, 1). We prove uniqueness and existence under the assumption that I - P is a nonsingular irreducible M-matrix, where I is the identity matrix and P = (p(ij)) with p(ij) greater than or equal to 0 (i, j = 1,..., N). (C) 2004 Elsevier Ltd. All rights reserved.