我們主要是研究下列型態的差分方程式，其中{c_(n)}是已知序列。設法找出解的充要條件。a_(n)=a_(n+1)-c_(n){[a_(n+1)]^2+α^2}

For sequence{c_(n)},we consider the following difference equation.a_(n)=a_(n+1)-c_(n){[a_(n+1)]^2+α^2}                     
   We will apply the method of backward induction to establish the existence and the uniqueness under certain conditions.

目錄
第一章  簡介..............................................1
第二章  差分方程式........................................4
第三章  特殊情況.........................................16
第四章  結論.............................................25
參考文獻.................................................26

參考文獻：
[1] On a difference equation with last conditions.  Differential equations and controltheory (Wuhan, 1994), 11--14, Lecture Notes in Pure and Appl. Math.,176,Dekker,New York, 1996.
[2] Chow,Y.S. and Robbins,H.(1966). A class of optimal stopping problems. Proc.Fifth Berkeley Symp.on Math. Stat. and Prob. Vol1.427-440.
[3] Chow,Y.S. and Robbins,H., and Siegmund,D.(1971). The theory of optimal stopping. Houghton Mifflin,Boston.
[4] Earl D. Rainville,Special Functions,Macmillan Company,New York,1971.