Positive solutions for 2nth-order singular sub-linear m-point boundary value problems

This paper investigates the existence of positive solutions for 2nth-order singular sub-linear m-point boundary value problems. Firstly, we establish a comparison theorem, then we define a partial ordering in C2n−2 [a, b] ∩ C2n(a, b) 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.