Abstract In this paper, we investigate some growth properties of meromorphic solutions of higher-order linear difference equation A n ⁢ ( z ) ⁢ f ⁢ ( z + n ) + … + A 1 ⁢ ( z ) ⁢ f ⁢ ( z + 1 ) + A 0 ⁢ ( z ) ⁢ f ⁢ ( z ) = 0 , A_{n}(z)f(z+n)+\dots+A_{1}(z)f(z+1)+A_{0}(z)f(z)=0, where A n ⁢ ( z ) , … , A 0 ⁢ ( z ) {A_{n}(z),\dots,A_{0}(z)} are meromorphic coefficients of finite φ-order in the complex plane where φ is a non-decreasing unbounded function. We extend some earlier results of Latreuch and Belaidi [Z. Latreuch and B. Belaïdi, Growth and oscillation of meromorphic solutions of linear difference equations, Mat. Vesnik 66 2014, 2, 213–222].

中文翻译：

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关于线性差分方程有限φ阶亚纯解的增长分析

摘要 在本文中，我们研究了高阶线性差分方程 A n ⁢ ( z ) ⁢ f ⁢ ( z + n ) + … + A 1 ⁢ ( z ) ⁢ f ⁢ ( z + 1 ) + A 0 ⁢ ( z ) ⁢ f ⁢ ( z ) = 0 , A_{n}(z)f(z+n)+\dots+A_{1}(z)f(z+1)+A_{ 0}(z)f(z)=0，其中 A n ⁢ ( z ) , … , A 0 ⁢ ( z ) {A_{n}(z),\dots,A_{0}(z)} 是亚纯的复平面中有限 φ 阶的系数，其中 φ 是一个非递减的无界函数。我们扩展了 Latreuch 和 Belaidi [Z. Latreuch 和 B. Belaïdi，线性差分方程亚纯解的增长和振荡，Mat。维斯尼克 66 2014, 2, 213–222]。