Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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DYNAMICS OF A HIGHER ORDER RATIONAL DIFFERENCE EQUATION

  • Wang, Yanqin (School of Physics & Mathematics, Jiangsu Polytechnic University)
  • Published : 2009.05.31
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Abstract

In this paper, we investigate the invariant interval, periodic character, semicycle and global attractivity of all positive solutions of the equation $Y_{n+1}\;=\;\frac{p+qy_{n-k}}{1+y_n+ry_{n-k}}$, n = 0, 1, ..., where the parameters p, q, r and the initial conditions $y_{-k}$, ..., $y_{-1}$, $y_0$ are positive real numbers, k $\in$ {1, 2, 3, ...}. It is worth to mention that our results solve the open problem proposed by Kulenvic and Ladas in their monograph [Dynamics of Second Order Rational Difference Equations: with Open Problems and Conjectures, Chapman & Hall/CRC, Boca Raton, 2002]

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References

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