
On Twopoint Boundary Value Problems for Secondorder Difference Equation 

View Full Text View/Add Comment Download reader 
KeyWord:Secondorder difference equation; Different boundary conditions; Boundary value problems 
Author Name  Affiliation  Huijuan Li  Department of Mathematics, Northwest Normal University, Lanzhou, Gansu 730070, China  Gaofeng Du  Department of Mathematics, Northwest Normal University, Lanzhou, Gansu 730070, China  Cunyan Yue  Department of Mathematics, Northwest Normal University, Lanzhou, Gansu 730070, China 

Hits: 26 
Download times: 94 
Abstract: 
In this paper, we aim to investigate the difference equation
\begin{align*}
\Delta^{2}y(t1)+y(t)=0, \ \ \ \ \ t\in[1,T]_{\mathbb{Z}}
\end{align*}
with different boundary conditions $y(0)=0$ or $\Delta y(0)=0$ and $y(T+1)=B$ or $\Delta y(T)=B$,\ where\ $T\geq 1$ is an integer and $B\in\mathbb{R}$. We will show that how the values of $T$ and $B$ influence the existence and uniqueness of the solutions to the about problem. In details, for the different problems, the $TB$plane explicitly divided into different parts according to the number of the solutions to the above problems. These parts of $TB$plane for the value of $T$ and $B$ guarantee the uniqueness, the existence and the nonexistence of solutions respectively. 


