Multiple rositive solutions for a three-point boundary value problem

We will find conditions on f that lead to the existence of at least three positive solutions to the three-point boundary value problem −x‴(t) + f (x(t)) = 0, with x(0) = x′(t2) = x″(1) = 0, on [0,1], where t2 ϵ [12,1). A positive solution will mean a solution in the cone of nonnegative functions in the Banach space C[0,1] with the sup norm.