Oscillation and asymptotic behaviour of a class of higher-order non-linear difference equations |
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| Authors: | H.A. El-Morshedy K. Gopalsamy |
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| Affiliation: | (1) Department of Mathematics, Damietta Faculty of Science, New Damietta 34517, Egypt, e-mail: elmorshedy@hotmail.com, EG;(2) Department of Mathematics and Statistics, The Flinders University of South Australia, GPO Box 2100, Adelaide 5001, Australia, AU |
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| Abstract: | The dynamical characteristics of scalar difference equations of the form?x n +1=f 1(x n −τ1)+f 2(x n −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. Received: September 5, 2001; in final form: March 7, 2002?Published online: April 14, 2003 |
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| Keywords: | Mathematics Subject Classification (2000). 39A11, 39A20, 92D25 . global attractivity – periodicity – oscillation – difference equation |
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