The method of lower and upper solutions for fourth order singular m-point boundary value problems

This paper investigates the existence of positive solutions for fourth order singular m-point boundary value problems. Firstly, we establish a comparison theorem, then we define a partial ordering in C2[0, 1] ∩ C4(0, 1) and construct lower and upper solutions to give a necessary and sufficient condition for the existence of C2[0, 1] as well as C3[0, 1] positive solutions. Our nonlinearity f (t, x, y) may be singular at x, y, t = 0 and/or t = 1. © 2005 Published by Elsevier Inc.