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Qualitative behavior of difference equation of order two and positive nonoscillatory solutions

$icon-email$ Khuong Vu Van , Thai Tran Hong

Abstract

In the paper we deal with the qualitative behavior of solutions of the following equation: $x_{n + 1} = a x_{n - 1} - \frac{b x_{n}^{2} + c x_{n - 1}^{2}}{1 - d x_{n} + e x_{n - 1}}, n = 0, 1, 2, \dots$ where the initial values $x_{- 1}, x 0$ are arbitrary positive numbers and $a, b, c, d, e$ are positive numbers. We also study the positive nonoscillatory solutions of the difference equation $x_{n + 1} = a x_{n - 1} - \frac{b x_{n}^{2} + a x_{n - 1}^{2}}{1 - c x_{n} + x_{n - 1}}, n = 0, 1, 2, \dots .$

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Qualitative behavior of difference equation of order two and positive nonoscillatory solutions

Abstract