ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR DIFFERENCE EQUATION <TEX>$x_{n+1}\;=\;{\alpha}\;+\;\beta{x_{n-1}}^{p}/{x_n}^p$</TEX>

Liu, Zhaoshuang; Liu, Zhaoshuang; Zhang, Zhenguo; Zhang, Zhenguo

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2024년 07월 03일(수) 13:30

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P-ISSN1226-0657
E-ISSN2287-6081
KCI

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ISSN : 1226-0657

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Vol.11 No.1

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ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR DIFFERENCE EQUATION <TEX>$x_{n+1}\;=\;{\alpha}\;+\;\beta{x_{n-1}}^{p}/{x_n}^p$</TEX>

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081

2004, v.11 no.1, pp.15-22

Liu, Zhaoshuang (College of Mathematics and Information Science, Hebei Normal University)
Zhang, Zhenguo (College of Mathematics and Information Science, Hebei Normal University)

Liu, Zhaoshuang, & Zhang, Zhenguo. (2004). ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR DIFFERENCE EQUATION <TEX>$x_{n+1}\;=\;{\alpha}\;+\;\beta{x_{n-1}}^{p}/{x_n}^p$</TEX>. 한국수학교육학회지시리즈B:순수및응용수학, 11(1), 15-22.

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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 <TEX>$x_{n+1}\;=\;{\alpha}\;+\;\beta{x_{n-1}}^{p}/{x_n}^p$</TEX> where <TEX>${\alpha}\;{\geq}\;0,\;{\beta}\;>\;0.\;<TEX>$\mid$</TEX>p<TEX>$\mid$</TEX>\;{\geq}\;1$</TEX>, and the initial conditions <TEX>$x_{-1}\;and\;x_0$</TEX> are arbitrary positive real numbers.

keywords: difference equation, stability, oscillation, period-2 solution

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논문 상세

Vol.11 No.1

ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR DIFFERENCE EQUATION <TEX>$x_{n+1}\;=\;{\alpha}\;+\;\beta{x_{n-1}}^{p}/{x_n}^p$</TEX>

Abstract

한국수학교육학회지시리즈B:순수및응용수학