Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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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)
  • Published : 2007.08.31
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Abstract

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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References

  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

Cited by

  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