时标上一类具p-Laplacian算子边值问题的交叉对称解

研究了时标上一类具p-Laplacian算子两点边值问题的交叉对称解,其中非线性项可能包含delta导数或nabla导数.通过引入一个伴随问题,得出一个动力方程的解与其伴随问题的解是交叉对称的.同时证明,如果非线性项包含delta导数或nabla导数,即使所研究的时标是等间距的,所得到的解也不一定是对称的.最后,给出了几个数值例子来说明主要结果.

Crossed Symmetric Solutions of the Boundary Value Problems with p-Laplacian on Time Scales

The cross symmetry properties of solutions for the two-point boundary value problems with p-Laplacian on time scales are considered.The nonlinear term may be relevant to the delta-derivative or the nabla-derivative.It is shown that,by introducing a proper companion problem,the solution of a dynamic equation is crossed symmetric to the solution of the companion problem.The investigation shows that if the nonlinear argument includes the terms of the delta-derivative or the nabla-derivative,even though the problems are difference problems on a uniform time scale,the solutions of them may be not symmetric.In addition, some computational examples are given to illustrate the main results.