Existence and uniqueness of solutions of (k+2)-point nonlocal boundary value problems for ordinary differential equations

Sufficient conditions are given under which the existence of solutions of 4-point nonlocal boundary value problems, for nth order nonlinear ordinary differential equations, yields the existence of unique solutions of (k+2)-point boundary value problems, for 1≤k≤n−1. The results are motivated by a Henderson and Jackson paper involving relationships between 2-point and n-point conjugate boundary value problems.