This paper studies the existence and uniqueness of solutions for the following nonlinear multi-point third-order boundary value problem (BVP):
where and are continuous functions. Assuming some monotonicity conditions on the functions the existence of a solution for the BVP (1.1) is proved by applying the method of lower and upper solutions, and Leray-Schauder degree theory.
In order to establish the uniqueness of the solution for BVP (1.1), the authors make use of the following auxiliary boundary value problem:
where with Some illustrative examples are also presented.