Expressions of solutions for a class of differential equations.

Elsayed, E.M.

Displaying similar documents to “Expressions of solutions for a class of differential equations.”

Solutions of the difference equation $x_{n + 1} = x_{n} x_{n - 1} - 1$ .

Kent, Candace M., Kosmala, Witold, Radin, Michael A., Stević, Stevo (2010)

Abstract and Applied Analysis

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On boundedness of solutions of the difference equation $x_{n + 1} = (p x_{n} + q x_{n - 1}) / (1 + x_{n})$ for $q > 1 + p > 1$ .

Xi, Hongjian, Sun, Taixiang, Yu, Weiyong, Zhao, Jinfeng (2009)

Advances in Difference Equations [electronic only]

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More on a rational recurrence relation.

Stević, Stevo (2004)

Applied Mathematics E-Notes [electronic only]

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On the rational recursive sequence $x_{n + 1} = \frac{α_{0} x_{n} + α_{1} x_{n - l} + α_{2} x_{n - k}}{β_{0} x_{n} + β_{1} x_{n - l} + β_{2} x_{n - k}}$

E. M. E. Zayed, M. A. El-Moneam (2010)

Mathematica Bohemica

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The main objective of this paper is to study the boundedness character, the periodicity character, the convergence and the global stability of positive solutions of the difference equation $x_{n + 1} = \frac{α_{0} x_{n} + α_{1} x_{n - l} + α_{2} x_{n - k}}{β_{0} x_{n} + β_{1} x_{n - l} + β_{2} x_{n - k}}, n = 0, 1, 2, \dots$ where the coefficients $α_{i}, β_{i} \in (0, \infty)$ for $i = 0, 1, 2,$ and $l$ , $k$ are positive integers. The initial conditions $x_{- k}, \dots, x_{- l}, \dots, x_{- 1}, x_{0}$ are arbitrary positive real numbers such that $l < k$ . Some numerical experiments are presented.