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On the positive nonoscillatory solutions of the difference equation x n+1 = α + \( \left( {\tfrac{{x_{n - k} }} {{x_{n - m} }}} \right) \) p

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Abstract

The aim of this paper is to show that the following difference equation:

$$ x_{n + 1} = \alpha + \left( {\tfrac{{x_{n - k} }} {{x_{n - m} }}} \right)^p ,n = 0,1,2,..., $$

where α > −1, p > 0, k,m ∈ N are fixed, 0 ≤ m < k, x −k , x −k+1, ..., x −m , ..., x −1, x 0 are positive, has positive nonoscillatory solutions which converge to the positive equilibrium \( \bar x \) = α + 1. It is interesting that the method described in the paper, in some cases can also be applied when the parameter α is variable.

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  1. Dept. of Math. Anal., Univ. of Transport and Communications, Hanoi City, Vietnam

    Khuong Van Vu

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  1. Khuong Van Vu
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Van Vu, K. On the positive nonoscillatory solutions of the difference equation x n+1 = α + \( \left( {\tfrac{{x_{n - k} }} {{x_{n - m} }}} \right) \) p . Appl. Math. J. Chin. Univ. 24, 45–48 (2009). https://doi.org/10.1007/s11766-009-1905-x

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  • DOI: https://doi.org/10.1007/s11766-009-1905-x

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