Boundedness and global attractivity of a higher-order nonlinear difference equation.

Jia, Xiu-Mei; Li, Wan-Tong

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Global asymptotic behavior of $y_{n + 1} = (p y_{n} + y_{n - 1}) / (r + q y_{n} + y_{n - 1})$ .

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Michal Čverčko (1975)

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Ethiraju Thandapani, L. Ramuppillai (1998)

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This paper deals with oscillatory and asymptotic behaviour of solutions of second order quasilinear difference equation of the form $Δ (a_{n - 1} | Δ y_{n - 1} |^{α - 1} Δ y_{n - 1}) + F (n, y_{n}) = G (n, y_{n}, Δ y_{n}), n \in N (n_{0}) (E)$ where $α > 0$ . Some sufficient conditions for all solutions of (E) to be oscillatory are obtained. Asymptotic behaviour of nonoscillatory solutions of (E) are also considered.

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Existence theorem for the difference equation $Y_{n + 1} - 2 Y_{n} + Y_{n - 1} = h^{2} f (y_{n})$ .

Weil, F. (1980)

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