Positive solutions of a nonlinear three-point boundary value problem

In this paper, by using the fixed-point index theorems, we study the existence of at least one or two positive solutions to the three-point boundary value problem y″(t) + a(t)f(y(t)) = 0, 0 < t < 1, y(0) = 0, y(1) = βy(η), where 0 < η < 1, 0 < β < 1/η. As an application, we also give some examples to demonstrate our results.