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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机译：摘要：形式为\ [\ Delta ^ m x_n = a_n \ varphi（x _ {\ tau _1（n）}，\ dots，x _ {\ tau _k（n）}）+ b_n的差分方程解的渐近性质\]正在研究中。获得条件，在该条件下，方程$ \ Delta ^ my_n = b_n $的每个（每个有界）解都渐近地等于上述方程的某些解。
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