A new comparison theorem and the solvability of a third-order two-point boundary value problem

A new comparison theorem is proved and then used to investigate the solvability of a third-order two-point boundary value problem u\u27 \u27 \u27 (t) + f (tu(t)u\u27 (t)u\u27 \u27 (t)) = 0, u(0) = u\u27 (2) = 0, u\u27 \u27 (0) = u\u27 \u27 (2?). Some existence results are established for this problem via upper and lower solutions method and xed point theory. 2010 Mathematics Subject Classication: 34B15, 34C0