On the growth of solutions of some second order linear differential equations with entire coefficients

Abstract

In this paper, we investigate the order and the hyper-order of growth of solutions of the linear differential equation where n≥ 2 is an integer, Aj (z)(≢ 0)(j= 1, 2) are entire functions with max {σ A (j):(j= 1, 2}< 1, Q (z)= q m z m+...+ q 1 z+ q 0 is a nonoonstant polynomial and a 1, a 2 are complex numbers. Under some conditions, we prove that every solution f (z)≢ 0 of the above equation is of infinite order and hyper-order 1.