Uniqueness implies existence for three-point boundary value problems for dynamic equations

AbstractShooting 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 × ℝ2 → ℝ is continuous, x1 < x2 < x3 in (a, b)T, y1, y2 ε ℝ, and T is a time scale. It is assumed such solutions are unique when they exist