摘要
The aim of this paper is to show that the following difference equation:Xn+1=α+(xn-k/xn-m)^p, n=0,1,2,…,where α 〉 -1, p 〉 O, k,m ∈ N are fixed, 0 ≤ m 〈 k, x-k, x-k+1,…,x-m,…,X-1, x0 are positive, has positive nonoscillatory solutions which converge to the positive equilibrium x=α+1. It is interesting that the method described in the paper, in some cases can also be applied when the parameter α is variable.
The aim of this paper is to show that the following difference equation:Xn+1=α+(xn-k/xn-m)^p, n=0,1,2,…,where α 〉 -1, p 〉 O, k,m ∈ N are fixed, 0 ≤ m 〈 k, x-k, x-k+1,…,x-m,…,X-1, x0 are positive, has positive nonoscillatory solutions which converge to the positive equilibrium x=α+1. It is interesting that the method described in the paper, in some cases can also be applied when the parameter α is variable.