Triple Solutions for Second-Order Three-Point Boundary Value Problems1

We establish the existence of at least three positive solutions to the second-order three-point boundary value problem, u + f t u = 0 u 0 = 0 αu η = u 1 , where η 0 < η < 1 0 < α < 1/η, and f 0 1 × 0 ∞ → 0 ∞ is continuous. We accomplish this by making growth assumptions on f which can apply to many more cases than the sublinear and superlinear ones discussed in recent works.