Global behavior of solutions of the nonlinear difference equation xn+1 = pn+xn-1/xn

被引：22

作者：

Devault, R ^{[1
]}

Kocic, VL

Stutson, D

机构：

[1] Northwestern State Univ Louisiana, Dept Math, Natchitoches, LA 71497 USA

[2] Xavier Univ Louisiana, Dept Math, New Orleans, LA 70125 USA

来源：

JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS | 2005年 / 11卷 / 08期

关键词：

nonautonomous difference equations; boundedness; attractivity; periodicity;

D O I：

10.1080/10236190500137405

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the global asymptotic behavior of solutions of the nonautonomous difference equation x(n+1) p(n) + x(n-1)/x(n) where {p(n)} is a positive bounded sequence and the initial conditions are positive. We obtain sufficient conditions for the boundedness and persistance of solutions and for the existence of unbounded solutions. In addition, we obtain global attractivity results. The results are applied to the case when {p(n)} is periodic with prime period k.

引用

页码：707 / 719

页数：13

共 9 条

[1] On the recursive sequence xn+1=α+xn-1/xn [J].

Amleh, AM ;

Grove, EA ;

Ladas, G ;

Georgiou, DA .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1999, 233 (02) :790-798

[2]

KUCZMA M, 1990, ENCY MATH ITS APPL

[3] On the dynamics of xn+1=pn+xn-1/xn-1 with a period-two coefficient [J].

Kulenovic, MRS ;

Ladas, G ;

Overdeep, CB .

JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2004, 10 (10) :905-914

[4] On the dynamics of Xn+1 = pn+Xn-1/Xn [J].

Kulenovic, MRS ;

Ladas, G ;

Overdeep, CB .

JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2003, 9 (11) :1053-1056

[5]

Kulenovic MRS, 2002, Dynamics of second order rational difference equations

[6]

Stevic S, 2003, DYNAM CONT DIS SER A, V10, P911

[7]

Stevic S., 2003, INT J MATH SCI, V2, P237

[8]

Zeidler E, 1991, APPL FUNCTIONAL ANAL

[9]

Zhao XQ., 2001, J DYN DIFFER SYST, V13, P107, DOI [DOI 10.1023/A:1009044515567, 10.1023/A:1009044515567]

← 1 →