Iteration for a Third-Order Three-Point BVP with Sign-Changing Green's Function

We are concerned with the following third-order three-point boundary value problem: u‴(t)=f(t,u(t)), t∈[0,1],u′(0)=u(1)=0, u″(η)+αu(0)=0, where α∈[0,2) and η∈[2/3,1). Although corresponding Green's function is sign-changing, we still obtain the existence of monotone positive solution under some suitable conditions on f by applying iterative method. An example is also included to illustrate the main results obtained