摘要
证明差分方程x_n=(A+x_(n-1)~p)/(B+x_(n-k)~p),n=0,1,2,…,(其中k≥2,A,B,p∈(0,+∞))在p^(k-1)≥k^k/(k-1)^(k-1)时,有无界的解,并且当p^(k-1)<k^k/(k-1)^(k-1)时,每个正解都有界.
Abstract:The difference equation Xn=A+xn-1^p/B+xn-k^p, n = 0,1,2, …, are considered in this paper, where k≥2 and A,B,p∈(0,+∞)). We show that if p^k-1≥k^k/(k-1)^k-1,then this equation has positive unbounded solutions,and if p^k-1≥k^k/(k-1)^k-1,then every positive solution of this equation is bounded
出处
《广西科学》
CAS
2008年第4期361-363,共3页
Guangxi Sciences
基金
Project supported by NSF of guangxi (0640205, 0728002)
innovation project of guangxi graduate education(20081505930701M43)
关键词
差分方程
有界性
正解
difference equation,boundedness, positive solution