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Zbl 1160.39306
Migda, Małgorzata; Migda, Janusz
Asymptotic properties of solutions of second-order neutral difference equations.
(English)
[J] Nonlinear Anal., Theory Methods Appl. 63, No. 5-7, A, e789-e799, electronic only (2005). ISSN 0362-546X

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.
MSC 2000:
*39A11 Stability of difference equations

Keywords: neutral difference equation; asymptotic behavior; nonoscillatory solution

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