Triple Solutions for Second-order Three-point Boundary Value Problems

Abstract 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, α u (η) =  u (1), where η: 0 lt; η  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.