Abstract
In first three sections, we are concerned with the existence and uniqueness of the solution of difference equations $\Delta ^{2}u_{k-1}+\lambda \left| u_{k}^{\gamma }\right| =0$, $k=1,2,...,n$ with the Dirichlet boundary condition: $u_{0}=u_{n+1}=0$ where $\lambda >0$ and $0<\gamma <1$. We found the solution is symmetry and gets large while one of the parameter $\lambda $, $\gamma $ and $n$ gets large.