Oscillation and asymptotic behaviour of a class of higher-order non-linear difference equations

被引：0
|
作者：
H.A. El-Morshedy
K. Gopalsamy
机构：
[1] Department of Mathematics,
[2] Damietta Faculty of Science,undefined
[3] New Damietta 34517,undefined
[4] Egypt,undefined
[5] e-mail: elmorshedy@hotmail.com,undefined
[6] Department of Mathematics and Statistics,undefined
[7] The Flinders University of South Australia,undefined
[8] GPO Box 2100,undefined
[9] Adelaide 5001,undefined
[10] Australia,undefined
来源：
Annali di Matematica Pura ed Applicata (1923 -) | 2003年 / 182卷 / 2期
关键词：
Mathematics Subject Classification (2000). 39A11, 39A20, 92D25 Key words. global attractivity – periodicity – oscillation – difference equation;
D O I：
10.1007/s10231-002-0058-9
中图分类号：
学科分类号：
摘要：
The dynamical characteristics of scalar difference equations of the form¶xn+1=f1(xn−τ1)+f2(xn−τ2),   n=0,1,2,...,¶are investigated. A necessary and sufficient condition is obtained for all positive solutions to be oscillatory about a unique positive equilibrium point and sufficient criteria for the global attractivity of the equilibrium are established. Also, the stability and periodicity of more general equations are studied via comparison with the corresponding properties of an associated first-order non-linear equation.
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页码：143 / 159
页数：16
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