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]∩C2n(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,x1,x2,…,xn) may be singular at xi=0,i=1,2,…,n,t=0 and/or t=1.