一类Lyness方程的一些性质(英文)

SOME PROPERTIES OF A KIND OF LYNESS EQUATION

本文主要研究下列Lyness方程的性质 :xn+1 =xn(a+b0 xn+b1 xn- 1 +… +bkxn-k)xn-k- 1,n =0 ,1 ,2 ,… ,( )其中a ,b0 ,b ,… ,bk ∈ [0 ,∞ ) ,a+∑ki=0bi >0 ,k∈ { 0 ,1 ,2 ,… } .文中给出了方程 ( )严格振动的充分条件 ,以及环长和环上极值的位置 .另外 ,还得到了方程 ( )在特殊情况下分别具有 4 ,5 ,6周期的必要充分条件 .

In this paper, the authors mainly investigate the properties of solutions of the following Lyness equation:x n+1 =x n(a+b 0x n+b 1x n-1 +...+b kx n-k )x n-k-1 , n=0,1,2,...,(*)where a,b 0,b 1,...,b k∈\[0,∞) with a+∑[DD(]ki=0b i>0, k∈{0,1,2,...}. Some sufficient conditions for the strict oscillation, the cycle length and the position of the extreme value in a semicycle of Eq.(*) are given. In addition, some necessary and sufficient conditions for the special cases of Eq.(*) t...