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) and others.