Abstract
By applying the Krasnoselskii fixed point theorem in cones and the fixed point index theory, we study the existence of positive solutions of the non linear third-order three point boundary value problem
u'"(t) + a(t) f(t, u(t)) = 0, t is an element of (0, 1),
u'(0) = u'(1) = alpha u(eta), u(01) = beta u(eta),
where alpha, beta and eta are constants with alpha is an element of [0, 1/n), and 0 < eta < 1. The results obtained here generalize the work of Torres [Positive solution for a third-order three point boundary value problem, Electronic J. Diff. Equ. 2013 (2013), 147, 1-11].