Growth properties of solutions of linear difference equations with coefficients having $\varphi$-order

Abstract

"In this paper, we investigate the relations between the growth of entire coefficients and that of solutions of complex homogeneous and non-homogeneous linear difference equations with entire coefficients of $% \varphi $-order by using a slow growth scale, the $\varphi $-order, where $% \varphi $ is a non-decreasing unbounded function. We extend some precedent results due to Zheng and Tu (2011) [15] and others."