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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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