EXISTENCE OF A POSITIVE SOLUTION FOR A THIRD-ORDER THREE POINT BOUNDARY VALUE PROBLEM

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].