Uniqueness and existence results for a third-order nonlinear multi-point boundary value problem

This paper provides sufficient conditions for the existence and uniqueness of solutions to a nonlinear multi-point boundary value problem for third order differentia equation. The nonlinear term f in the differential equation under consideration may depend on second-order derivative. The emphasis here is the boundary conditions are nonlinear and this is where the main novelty of this work lies. By applying the upper and lower solutions method, as well as degree theory, the existence and uniqueness results of the problem are established. Some examples are given to demonstrate the main results.