In this paper we are concerned with uniqueness implies uniqueness and uniqueness implies existence questions for solutions of a class of boundary value problems for the third order ordinary differential equation (ODE). First we show uniqueness of solutions of a class of two-point problems implies the uniqueness of solutions of an associated class of three-point problems. Then we establish uniqueness of solutions of the class of two-point problems implies the existence of solutions of the class of two point problems and the associated class of three-point problems.
Respress, Veronica, "Uniqueness of Solutions Implies Existence and Uniqueness of Solutions of Boundary Value Problems for Third Order Differential Equations" (2010). Undergraduate Mathematics Day: Proceedings and Other Materials. 25.