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Asymptotic properties of nonoscillatory solutions of higher order neutral difference equations. (English) Zbl 1131.39008
We study asymptotic behavior of solutions of a higher order neutral difference equation of the form
\[ \Delta^m(x_n+p_nx_{n-\tau})+f(n,x_{\sigma(n)})=h_n. \]
We present conditions under which all nonoscillatory solutions of the above equation have the property \(x_n = cn^{m-1}+o(n^{m-1})\) for some \(c\in R\).

MSC:
39A11 Stability of difference equations (MSC2000)
39A10 Additive difference equations
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