A classification scheme for nonoscillatory solutions of a higher order neutral difference equation.

Zhu, Zhi-Qiang; Wang, Gen-Qiang; Cheng, Sui Sun

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A classification scheme for the eventually positive solutions of a class of higher order nonlinear difference equations is given in terms of their asymptotic magnitudes, and necessary as well as sufficient conditions for the existence of such solutions are provided.

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Asymptotic properties of solutions of higher order difference equations

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Asymptotic properties of solutions of the difference equation of the form $Δ^{m} x_{n} = a_{n} ϕ (x_{τ_{1} (n)}, \dots, x_{τ_{k} (n)}) + b_{n}$ are studied. Conditions under which every (every bounded) solution of the equation $Δ^{m} y_{n} = b_{n}$ is asymptotically equivalent to some solution of the above equation are obtained.

Existence of nonoscillatory solutions of some higher order difference equations.

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