On the hyper-order of transcendental meromorphic solutions of certain higher order linear differential equations

Abstract

In this paper, we investigate the growth of meromorphic solutions of the linear differential equation f (k) + hk−1(z)ePk−1(z) f (k−1) + . . . + h0(z)eP0(z) f = 0, where k 2 is an integer, Pj(z) (j = 0, 1, . . . , k − 1) are nonconstant polynomials and hj(z) are meromorphic functions. Under some conditions, we determine the hyper-order of these solutions. We also consider nonhomogeneous linear differential equations.