关于差分方程χn=A+χpn-1/B+χpn-k正解的有界性

摘要

The difference equation χn=A+χpn-1/B+χpn-k,n＝0,1,2,…,are considered in this paper,where k≥2 and A,B,p∈(0,+∞). We show that if pk-1≥kk/(k-1)k-1, then this equation has positive unbounded solutions,and if pk-1＜kk/(k-1)k-1, then every positive solution of this equation is bounded.%证明差分方程 χn=A+χpn-1/B+χpn-k,n＝0,1,2,...,(其中k≥2,A,B,p∈(0,+∞))在pk-1≥kk/(k-1)k-1时,有无界的解,并且当pk-1＜kk/(k-1)k-1时,每个正解都有界.