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Asymptotic properties of solutions of second-order neutral difference equations. (English) Zbl 1160.39306
Summary: We study asymptotic behavior of solutions of second-order neutral difference equation $$\Delta^{2}(x_n+px_{n-k})+f(n,x_n)=0$$.We present conditions under which all nonoscillatory solutions of the above equation have the property $$x_n=cn+o(n)$$ for some $$c \in \mathbb{R}$$ as well as sufficient conditions under which all nonoscillatory solutions are asymptotically linear.

##### MSC:
 39A11 Stability of difference equations (MSC2000)
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##### References:
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