Existence-uniqueness and iterative methods for third-order boundary value problems

In this paper we shall provide necessary and sufficient conditions for the existence and uniqueness of solutions of third-order nonlinear differential equations satisfying three-point boundary conditions. For the linear case, we propose a constructive method which is a variation of the method of chasing. For the nonlinear problems sufficient conditions are provided to ensure the convergence of a general class of iterative methods. Several examples are also included.