On the trichotomy character of Xn+1=(α+βXn+γXn-1)/A+Xn

被引：52

作者：

Gibbons, CH

Kulenovic, MRS

Ladas, G ^{[1
]}

Voulov, HD

机构：

[1] Univ Rhode Isl, Dept Math, Kingston, RI 02881 USA

[2] So Illinois Univ, Dept Math, Carbondale, IL 62901 USA

来源：

JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS | 2002年 / 8卷 / 01期

关键词：

boundedness; difference equation; global attractivity; global asymptotic stability; period two solutions; trichotomy of solutions;

D O I：

10.1080/10236190211940

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that the equation in the title with nonnegative parameters and nonnegative initial conditions exhibits a trichotomy character concerning periodicity, convergence, and boundedness which depends on whether the parameter gamma is equal, less, or greater than the sum of the parameters beta and A.

引用

页码：75 / 92

页数：18

共 10 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]

[Anonymous], 1995, J DIFFER EQUATIONS A

[3]

Gibbons C.H., 2000, Math. Sci. Res. Hot-line, V4, P1

[4]

GIBBONS CH, 2000, IN PRESS P 5 INT C D

[5]

Grove EA, 2000, COMMUNICATIONS IN DIFFERENCE EQUATIONS, P149

[6]

KOCIC VL, 1993, GLOBAL BEHAV NONLINE

[7] On the recursive sequence xn+1=(αxn+βxn-1)/(A+xn) [J].

Kulenovic, MRS ;

Ladas, G ;

Prokup, NR .

JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2000, 6 (05) :563-576

[8] On period two solutions of -: xn+1=α+βxn+γxn-1/A+Bxn+Cxn-1 [J].

Kulenovic, MRS ;

Ladas, G .

JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2000, 6 (05) :641-646

[9]

KULENOVIC MRS, IN PRESS DYNAMICS 2

[10] Open problems and conjectures [J].

Ladas, G .

JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 1999, 5 (02) :211-215

← 1 →