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Uniqueness implies existence for three-point boundary value problems for dynamic equations |
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| Authors: | J. Henderson C.C. Tisdell W.K.C. Yin |
| Affiliation: | 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, 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 |
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