Positive Solutions of a Singular Third-Order m-Point Boundary Value Problem

This paper is concerned with the existence and nonexistence of positive solutions to the singular third-order m-point boundary value problem u'''(t) + a(t)f(u(t)) = 0, 0 < t < 1, u(0) = u'(0) = 0, u'(1) - Sigma(m-2)(i=1) alpha(i)u'(xi(i)) = lambda, where xi(i) epsilon [0, 1), alpha(i) epsilon [0, infinity) (i = 1, 2, ... ,m-2) are constants lambda epsilon (0,1) is a parameter, f : [0, infinity) -> [0, infinity) is continuous and a(.) is allowed to be singular at t = 0 and t = 1. The results here essentially extend and improve some known results.