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) - + i = 1 m - 2 α i u ' ( i) =,where i ⋯ [ 0,1),α i ⋯ [ 0,∞) (i = 1,2,.,m - 2) are constants,⋯ (0,1) is a parameter,f: [ 0,∞) → [ 0,∞) 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. © 2013 shaolin zhou and xiaoling han.