Positive solution for three-point boundary value problems with sign changing nonlinearities Original Research Article

By constructing available operators, some new existence theorems of positive solutions are obtained for a class of three-point boundary value problems u″ + λh(t)f(t, u) = 0, 0 ≤ t ≤ 1, u(0) − βu′(0) = 0, u(1) = αu(η), where f is allowed to change sign, η ϵ (0, 1). The associated Greenʹs function for the above problem is also given.