A class of 2nth-order singular boundary value problems

This paper investigates the existence of positive solutions for 2nth-order (n > 1) singular sub-linear boundary value problems. First of all, we establish the maximal principle and some important lemmas. Then, we define a partial ordering in C2n-2 [0, 1] boolean AND C-2n (0, 1) and construct lower and upper solutions to give a necessary and sufficient condition for the existence of C2n-2[0, 1] as well as C2n-1[0, 1] positive solutions. Our nonlinearity f (t, x(1), x(2),...,x(n)) may be singular at x(i) = 0, i = 1, 2,...,n, t = 0 and/or t = 1. (c) 2006 Elsevier Ltd. All rights reserved.