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Dedicated to Allan Peterson on the occasion of his 60th birthday. In this paper, we explore crossed symmetry properties of the solutions of second-order nonlinear boundary value problems on time scales (BVPTS). Dynamic equations under delta and nabla differentiations are considered. It is proven that, by introducing a proper companion problem, the solution of a dynamic equation and its associated Green's functions are crossed symmetric in connection with those of the companion problem, respectively. Proper jump functions on time scales are utilized. Computational examples are given to further illustrate our conclusions.
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Eloe et al. (2003) studied this question.
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