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BEHAVIOR OF POSITIVE SOLUTIONS OF A DIFFERENCE EQUATION

  • TOLLU, D.T. (Department of Mathematics-Computer Sciences, Faculty of Sciences, Necmettin Erbakan University Meram Campus) ;
  • YAZLIK, Y. (Department of Mathematics, Faculty of Science and Art, Nevsehir Haci Bektas Veli University) ;
  • TASKARA, N. (Department of Mathematics, Faculty of Science, Selcuk University)
  • Received : 2015.12.05
  • Accepted : 2017.01.29
  • Published : 2017.05.30

Abstract

In this paper we deal with the difference equation $$y_{n+1}=\frac{ay_{n-1}}{by_ny_{n-1}+cy_{n-1}y_{n-2}+d}$$, $$n{\in}\mathbb{N}_0$$, where the coefficients a, b, c, d are positive real numbers and the initial conditions $y_{-2}$, $y_{-1}$, $y_0$ are nonnegative real numbers. Here, we investigate global asymptotic stability, periodicity, boundedness and oscillation of positive solutions of the above equation.

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