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

Authors:	J Henderson CC Tisdell WKC Yin

Institution:	Department of MathematicsBaylor University Waco, TX 76798-7328, U.S.A. School of MathematicsThe University of New South Wales UNSW Sydney 2052, Australia Department of MathematicsLaGrange College LaGrange, GA 30240, U.S.A.

Abstract:	Shooting methods are used to obtain solutions of the three-point boundary value problem for the second-order dynamic equation, y^ΔΔ = f (x, y, y^Δ), 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
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