一个猜想的证明

The confirmation of a conjecture

考察下述差分方程xn+1=xn-1/p+xn,n=0,1,…,其中p>0,初始条件x-1,x0是任意非负实数。证明了由M.R.S.Kulenovic和G.Ladas在《二阶有理差分方程动力学开问题及猜想》一书中所提的猜想4.8.2。

The following difference equation will be investigated： xn＋1=xn-1/p＋xn,n=0,1,…,where p〉0 and the initial conditions are arbitrary non-negative real numbers. The conjecture 4.8.2 will be confirmed which was proposed by M. R. S. Kulenovic and G. Ladas in [Dynamics of Second Order Rational Difference Equations, with Open Problems and Conjectures, Chapman ＆ Hall/GRC Press, 2001].