Positive solution of singular Dirichlet boundary value problems for second order differential equation system ✩

This paper investigates the existence of positive solutions of singular Dirichlet boundary value problems for second order differential system. A necessary and sufficient condition for the existence of C[0, 1] × C[0, 1] positive solutions as well as C1[0, 1]×C1[0, 1] positive solutions is given by means of the method of lower and upper solutions and the fixed point theorems. Our nonlinearity fi (t, x1, x2) may be singular at x1 = 0, x2 = 0, t = 0 and/or t = 1, i = 1, 2. © 2006 Elsevier Inc. All rights reserved.