Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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ON THE DIFFERENCE EQUATION $x_{n+1}=\frac{a+bx_{n-k}-cx_{n-m}}{1+g(x_{n-l})}$

  • Zhang, Guang (School of Science, Tianjin University of Commerce) ;
  • Stevic, Stevo (Mathematical Institute of the Serbian Academy of Science)
  • Published : 2007.09.30

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Abstract

In this paper we consider the difference equation $$x_{n+1}=\frac{a+bx_{n-k}\;-\;cx_{n-m}}{1+g(x_{n-l})}$$ where a, b, c are nonegative real numbers, k, l, m are nonnegative integers and g(x) is a nonegative real function. The oscillatory and periodic character, the boundedness and the stability of positive solutions of the equation is investigated. The existence and nonexistence of two-period positive solutions are investigated in details. In the last section of the paper we consider a generalization of the equation.

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