Growth of Meromorphic Solutions of a class of Higher Order Linear Differential Equations

Abstract

In this paper, we investigate the order and the hyper-order of meromorphic solutions of the linear differential equation  f^{(k)}+∑(B_{j}e^{P_{j}(z)}+D_{j}e^{R_{j}(z)})f^{(j)}+(Aâ‚e^{Qâ‚(z)}+Aâ‚‚e^{Qâ‚‚(z)})f=0,where Q_{s}(z) (s=1,2), P_{j}(z), R_{j}(z) (j=1,...,k-1) are nonconstant polynomials and A_{s}(z) (s=1,2), B_{j}(z), D_{j}(z) (j=1,...,k-1) are meromorphic functions (≡0). Under some conditions, we prove that every meromorphic solution f(≡0) of the above equation is of infinite order and we give an estimate of its hyper-order.