Some properties of meromorphic solutions of logarithmic order to higher order linear difference equations

This paper is devoted to the study of the growth of solutions of the linear difference equation
\begin{gather*} A_n(z)f(z+n)+A_{n-1}(z)f(z+n-1)\\ +\dots+A_1(z)f(z+1)+A_0(z)f(z)=0, \end{gather*}
where $A_n(z),\dots,A_0(z)$ are entire or meromorphic functions of finite logarithmic order. We extend some precedent results due to Liu and Mao, Zheng and Tu, Chen and Shon and others.