Positive solutions of second-order three-point boundary value problems with change of sign

We study the existence of positive solutions of the second-order three-point boundary value problems ′(t) + λa(t)f(y(t)) = 0, 0 < t < 1, y(0) = (0), y(1) = βy(n) where 0 < β < 1, 0 < η < 1. We show the existence of at least one positive solution by applying the Krasnoselskii fixed-point theorem in a cone, here a(t) is allowed to changes sign on [0, 1]. Applications of our results are provided to yield positive radial solutions of some elliptic boundary value problems on an annulus.