The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
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ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR DIFFERENCE EQUATION $x_{n+1}\;=\;{\alpha}\;+\;\beta{x_{n-1}}^{p}/{x_n}^p$

  • Liu, Zhaoshuang (College of Mathematics and Information Science, Hebei Normal University) ;
  • Zhang, Zhenguo (College of Mathematics and Information Science, Hebei Normal University)
  • Published : 2004.02.01
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Abstract

In this paper, we investigate asymptotic stability, oscillation, asymptotic behavior and existence of the period-2 solutions for difference equation $x_{n+1}\;=\;{\alpha}\;+\;\beta{x_{n-1}}^{p}/{x_n}^p$ where ${\alpha}\;{\geq}\;0,\;{\beta}\;>\;0.\;$\mid$p$\mid$\;{\geq}\;1$, and the initial conditions $x_{-1}\;and\;x_0$ are arbitrary positive real numbers.

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