Uniqueness implies existence and uniqueness conditions for nonlocal boundary value problems for nth order differential equations

For the nth order differential equation, y(n) = f (x, y,y , . . . , y(n−1)), we consider uniqueness implies existence results for solutions satisfying certain nonlocal (k +2)-point boundary conditions, 1 k n−1. Uniqueness of solutions when k = n−1 is intimately related to uniqueness of solutions when 1 k n−2. These relationships are investigated as well. © 2006 Elsevier Inc. All rights reserved