Uniqueness implies existence for three-point boundary value problems for second order differential equations

Shooting methods are employed to obtain solutions of the three-point boundary value problem for the second order equation, y '' = f (x, y, y'), y(x(1)) = y(1), y(x(2)) - y(x(3)) = y(2), where f : (a, b) x R-2 -> R is continuous, alpha < x(1) < x(2) < x(3) < b, and y(1), y(2) is an element of R, and it is assumed that solutions of such problems are unique, when they exist. (c) 2005 Elsevier Ltd. All rights reserved.