Dynamic Systems and Applications
In this paper we continue to explore cross-symmetry properties of the solutions of second-order nonlinear boundary value problems on time scales. 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 is cross-symmetric to the solution of the companion problem. Proper jump functions on time scales are utilized. Computational examples are given to further illustrate our conclusions.
Eloe, Paul W. and Sheng, Qin, "A continuation of the discussion on cross symmetry of solutions" (2003). Mathematics Faculty Publications. 83.