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Asymptotic properties of solutions of higher order difference equations. (English) Zbl 1224.39021
Summary: Asymptotic properties of solutions of the difference equation $$\Delta ^m x_n=a_n\varphi (x_{\tau _1(n)},\dots ,x_{\tau _k(n)})+b_n$$ are studied. Conditions under which every (every bounded) solution of the equation $$\Delta ^{m}y_{n}=b_{n}$$ is asymptotically equivalent to some solution of the above equation are obtained.

##### MSC:
 39A22 Growth, boundedness, comparison of solutions to difference equations 39A10 Additive difference equations
##### Keywords:
difference equation; asymptotic behavior; bounded solution
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