On 2 nth-order nonlinear multi-point boundary value problems

This paper is concerned with the existence and uniqueness of a solution for a class of 2 nth-order nonlinear multi-point boundary value problems. The existence of a solution is proven by the method of upper and lower solutions without any monotone condition on the nonlinear function. A sufficient condition for the uniqueness of a solution is given. It is also shown that there exist two sequences which converge monotonically from above and below, respectively, to the unique solution. Two examples are presented to illustrate the results.