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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 $c \in \bbfR$ as well as sufficient conditions under which all nonoscillatory solutions are asymptotically linear.

39A11Stability of difference equations (MSC2000)
Full Text: DOI
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