On the meromorphic solutions of linear differential equations

Abstract

In this paper, we investigate the growth of meromorphic solutions of higher order linear differential equation f (k)+Ak−1(z)e Pk−1(z) f (k−1)+· · ·+A1(z)e P1(z) f 0+A0(z)e P0(z) f = 0 (k ≥ 2), where Pj (z) (j = 0, 1, · · · , k − 1) are nonconstant polynomials such that deg Pj = n (j = 0, 1, · · · , k − 1) and Aj (z)(6≡ 0) (j = 0, 1, · · · , k − 1) are meromorphic functions with order ρ(Aj ) < n (j = 0, 1, · · · , k − 1).