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Keywords:
difference equation; asymptotic behavior
Summary:
Asymptotic properties of solutions of the difference equation of the form \[ \Delta ^m x_n=a_n\varphi (x_{\tau _1(n)},\dots ,x_{\tau _k(n)})+b_n \] are studied. Conditions under which every (every bounded) solution of the equation $\Delta ^my_n=b_n$ is asymptotically equivalent to some solution of the above equation are obtained.\\
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