Infinite order of transcendental meromorphic solutions of some nonhomogeneous linear differential equations

Abstract

In this paper, we investigate the order of growth of transcendental meromorphic
solutions of the linear dierential equation

$f^{(k)}+\sum_{j=0}^{k-1} hj(z) e^{Pj(z) } f^{(j)}=F$

where k>=2 is an integer, Pj (z) (j = 0,...,k-1) are nonconstant polynomials, hj (z) (j =0; :::; k 􀀀 1) and F (≠0) are meromorphic functions. Under some conditions, we prove that every transcendental meromorphic solution of the above equation is of infinite order.