Journal of Applied Mathematics and Computing

, Volume 38, Issue 1, pp 173–180

Dynamics of the max-type difference equation \(x_{n}=\max\{\frac{ 1}{ x_{n-m}} , \frac{A_{n} }{x_{n-r} }\}\)

Article

DOI: 10.1007/s12190-010-0471-y

Cite this article as:
Sun, T., Xi, H., Han, C. et al. J. Appl. Math. Comput. (2012) 38: 173. doi:10.1007/s12190-010-0471-y
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Abstract

In this paper, we study the periodicity, the boundedness and the convergence of the following max-type difference equation
$$x_n =\max\biggl\{\frac{ 1}{ x_{n-m}} , \frac{A_n }{x_{n-r} }\biggr \},\quad n =0, 1,2,\ldots,$$
where \(\{A_{n}\}^{+\infty}_{n=0}\) is a periodic sequence with period k and An∈(0,1) for every n≥0, m∈{1,2} and r∈{2,3,…} with m<r, the initial values xr,…,x−1∈(0,+∞). The special case when \(m = 1, r = 2, \{A_{n}\}^{+\infty}_{ n=0}\) is a periodic sequence with period k and An∈(0,1) for every n≥0 has been completely investigated by Y. Chen. Here we extend his results to the general case.

Keywords

Max-type difference equation Positive solution Periodicity 

Mathematics Subject Classification (2000)

39A10 39A11 

Copyright information

© Korean Society for Computational and Applied Mathematics 2010

Authors and Affiliations

  • Taixiang Sun
    • 1
  • Hongjian Xi
    • 2
  • Caihong Han
    • 1
  • Bin Qin
    • 2
  1. 1.College of Mathematics and Information ScienceGuangxi UniversityNanningChina
  2. 2.Department of MathematicsGuangxi College of Finance and EconomicsNanningChina

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