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

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 lt; 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.