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 ${f^{( k) }+A_{k-1}( z)e^{P_{k-1}( z) }f^{( k-1)}+\cdots+A_{1}( z) e^{P_{1}( z) }f'+A_{0}( z)e^{P_{0}( z) }f=0 ( k\geq 2)}$ , where ${P_{j}( z) ( j=0,1,\cdots,k-1)}$ are nonconstant polynomials such that deg ${P_{j}=n ( j=0,1,\cdots,k-1)}$ and ${A_{j}( z) (\not\equiv 0) ( j=0,1,\cdots,k-1)}$ are meromorphic functions with order ${\rho ( A_{j}) < n ( j=0,1,\cdots,k-1) }$.