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doi:10.1016/j.am1.2003.08.015 
Copyright © 2004 Published by Elsevier Ltd.
Uniqueness implies existence for three-point boundary value problems for dynamic equations
J. Henderson
, C.C. Tisdell and W.K.C. Yin
Accepted 1 August 2003.
Available online 18 January 2005.
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Abstract
Shooting methods are used to obtain solutions of the three-point boundary value problem for the second-order dynamic equation, yΔΔ = f (x, y, yΔ), y(x1) = y1, y(x3) − y(x2) = y2, where f : (a, b)T × 
2 → is continuous, x1 < x2 < x3 in (a, b)T, y1, y2 ε , and T is a time scale. It is assumed such solutions are unique when they exist.
Keywords: Time scale; Boundary value problem; Dynamic equation; Shooting method
