Article
MSC:
34C99,
39A10,
39A11,
39A20,
39A22,
39A23,
39A30,
39A99 | MR 2494777 | Zbl 1199.39025 | DOI: 10.21136/MB.2008.140612
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Keywords:
difference equations; boundedness character; period two solution; convergence; global stability
difference equations; boundedness character; period two solution; convergence; global stability
Summary:
The main objective of this paper is to study the boundedness character, the periodic character, the convergence and the global stability of positive solutions of the difference equation \[ x_{n+1}=\bigg ( A+\sum _{i=0}^k\alpha _ix_{n-i}\bigg ) \Big / \sum _{i=0}^k\beta _ix_{n-i},\ \ n=0,1,2,\dots \] where the coefficients $A$, $\alpha _i$, $\beta _i$ and the initial conditions $x_{-k},x_{-k+1},\dots ,x_{-1},x_0$ are positive real numbers, while $k$ is a positive integer number.
References:
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