一般Lyness方程的周期性与严格振动性的注记

NOTES ON PERIODICITY AND STRICT OSCILLATION FOR GENERALIZED LYNESS EQUATION

研究一般 Lyness方程 xn+ 1=cxn+d( a+bxn) xn-1,n=0 ,1 ,2 ,…周期性与振动性 ,其中 a,b,c,d∈ [0 ,+∞ )且 a+b>0 ,c+d>0 ,初值 x-1,x0 为任意正数 .作为应用 ,主要讨论以下方程 :xn+ 1=max{cxn,d}max{a,bxn}xn-1,n=0 ,1 ,2 ,… 的周期性与振动性 .

A generalized Lyness equation is investigated,that is x n+1 =cx n+d(a+bx n)x n-1 ,n=0,1,2,… where a,b,c,d∈[0,+∞),a+b>0,c+d>0 and the initial values x -1 ,x 0 can be arbitrary positive numbers.As an application,periodicity and oscillation of the equation x n+1 =max｛cx n,d｝max｛a,bx n｝x n-1 ,n=0,1,2,… are mainly discussed.