대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제44권3호
  • /
  • Pages.439-445
  • /
  • 2007
  • /
  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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GLOBAL ASYMPTOTIC STABILITY OF A HIGHER ORDER DIFFERENCE EQUATION

  • Hamza, Alaa E. (DEPARTMENT OF MATHEMATICS FACULTY OF SCIENCE, CAIRO UNIVERSITY) ;
  • Khalaf-Allah, R. (DEPARTMENT OF MATHEMATICS FACULTY OF SCIENCE, HELWAN UNIVERSITY)
  • 발행 : 2007.08.31
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초록

The aim of this work is to investigate the global stability, periodic nature, oscillation and the boundedness of solutions of the difference equation $$x_{n+1}={\frac{Ax_{n-1}}{B+Cx_{n-2}{\iota}x_{n-2k}$$, n = 0, 1, 2,..., where A, B, C are nonnegative real numbers and $\iota$, k are nonnegative in tegers, $\iota{\leq}k$.

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참고문헌

  1. C. Cinar, On the positive solution of the difference equation $x_n+1=frac-ax_-n-1}}-1+bx_nx-n-1}}$, Appl.Math. Comput. 156 (2004), no. 2, 587-590 https://doi.org/10.1016/j.amc.2003.08.010
  2. V. L. Kocic and G. Ladas, Global behavior of nonlinear difference equations of higher order with applications, Mathematics and its Applications, 256. Kluwer Academic Publishers Group, Dordrecht, 1993
  3. R. E. Mickens, Difference equations, Theory and applications. Second edition. Van Nostrand Reinhold Co., New York, 1990
  4. X. Yang, W. Su, B. Chen, G. M. Megson, and D. J. Evans, On the recursive sequence $x_-n+1}=frac-ax_n+bx_-n-1}-c+dx_nx_-n-1}}$, Appl. Math. Comput. 162 (2005), no. 3, 1485-1497 https://doi.org/10.1016/j.amc.2004.03.023

피인용 문헌

  1. On the Difference equation xn+1=axn−l+bxn−k+cxn−sdxn−s−e vol.40, pp.3, 2017, https://doi.org/10.1002/mma.3980