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

摘要

In this paper, we investigate the growth of meromorphic solutions of the linear differential equation [f^{(k)}+h_{k-1}(z)e^{P_{k-1}(z)}f^{(k-1)}+ldots +h_{0}(z)e^{P_{0}(z)}f=0,] where (kgeq 2) is an integer, (P_{j}(z)) ((j=0,1,ldots ,k-1)) are nonconstant polynomials and (h_{j}(z)) are meromorphic functions. Under some conditions, we determine the hyper-order of these solutions. We also consider nonhomogeneous linear differential equations.