On the hyper-order of solutions of a class of higher order linear differential equations

Abstract

In this paper, we investigate the growth of solutions of the linear differential equation f (k) +

Ak−1(z)e Pk−1(z) + Bk−1 (z)

f (k−1) + · · · +

A1(z)e P1(z) + B1 (z)

f ′ +

A0(z)e P0(z) + B0 (z)

f = 0, where k ≥ 2 is an integer, Pj(z) (j = 0, 1, · · · , k − 1) are nonconstant polynomials and Aj(z) (6≡ 0), Bj (z) (6≡ 0) (j = 0, 1, · · · , k − 1) are meromorphic functions. Under some conditions, we determine the hyper-order of these solutions.