一類差分方程的奇點集和解的全局性

全衛(wèi)貞

(湛江師范學(xué)院基礎(chǔ)教育學(xué)院，廣東湛江 524037)

一類差分方程的奇點集和解的全局性

全衛(wèi)貞

(湛江師范學(xué)院基礎(chǔ)教育學(xué)院，廣東湛江 524037)

差分方程；奇點集；平衡解；二周期解；全局性

[1]中，Ladas研究了Riccati差分方程

在參考文獻(xiàn)[3]中，駱元媛研究了三階差分方程

1 預(yù)備知識

2 主要結(jié)果

參考文獻(xiàn)

[1] Ladas G, Kulenovic M R S. Dynamics of the second rational difference equations with open problems and conjectures [M]. New York: Chapman and Hall / CRC, 2002: 17-24.

[2] Sedaghat H. On third-order rational difference equations with quadratic terms [J]. Journal of Difference Equations and Applications, 2008, 8: 889-897.

[3] 駱元媛. 一類有理差分方程解的全局行為[D]. 四川: 四川大學(xué)數(shù)學(xué)學(xué)院, 2012: 8-34.

[4] 完巧玲. 差分方程解的全局穩(wěn)定性[J]. 隴東學(xué)院學(xué)報, 2012, 20(2): 6-8.

[5] Dehghan M. Global behaviour of the Riccati difference equation of order two [J]. Journal of Difference Equations and Applications, 2011, 4: 467-477.

[6] Elsayed E M. Qualitative behaviour of difference equation of order two [J]. Mathematical and Computer Modelling, 2009, 50: 1130-1141.

[7] Kelley W G, Peterson A C. Difference Equations with Applications [M]. New York: Academic Press, 1991: 1-98.

[8] Kocic V L, Ladas G. Global behavior of nonlinear difference equations of higher order with applications [M]. Dordrecht: Kluwer Academic Publishers, 1993: 1-121.

[9] Cinar C. On the positive solutions of the difference equation [J]. Applied Mathematics and Computation, 2004, 156: 587-590.

[10] Camouzis E, Ladas G. When does local asymptoic stability imply global attractivity in rational equations [J]. Journal of Difference Equations and Applications, 2006, 12: 863-885.

[11] Sun T X, Xi H J. The periodic character of the difference equation[J]. Advances in Difference Equations, 2008, DOI: 10.1155/2008/143723.

[12] Yu J S, Wang Z C. Asymptotic behavior and oscillation delay difference equations [J]. Funkcial Eekvac, 1994, 37: 241-249.

The Forbidden Set and the Global Behavior of Solutions of a Difference Equation

QUAN Weizhen
(College of Basic Education, Zhanjiang Norman University, Zhanjiang, China 524037)

Difference Equation; Forbidden Set; Equilibrium Solution; Period-two Solution; Global Behavior

O175.12

A

1674-3563(2013)03-0011-06

10.3875/j.issn.1674-3563.2013.03.003 本文的PDF文件可以從xuebao.wzu.edu.cn獲得

(編輯：王一芳)

2012-10-18

湛江師范學(xué)院青年項目(QL1021)

全衛(wèi)貞(1980- )，女，廣西玉林人，講師，碩士，研究方向：差分方程與動力系統(tǒng)

近些年來，差分方程理論引起了許多學(xué)者、專家的重視，已成為現(xiàn)代數(shù)學(xué)的一個研究熱點．Ladas等人在文獻(xiàn)[1]中提出了關(guān)于差分方程的公開問題和猜想；另外，差分方程的奇點集和解的有界性、收斂性、穩(wěn)定性、周期性等動力學(xué)性質(zhì)也得到了人們的廣泛關(guān)注，并獲得很多的研究成果[1-12]．