On Complex Oscillation Theory of Solutions of Some Higher Order Linear Differential Equations

摘要

In this paper,we shall use Nevanlinna theory of meromorphic functions to investigate the complex oscillation theory of solutions of some higher order linear differential equation.Suppose that A is a transcendental entire function with ρ（A）＜1/2.Suppose that k≥2 and f（k）+A（z）f=0 has a solution f with λ（f）＜ρ（A）,and suppose that A1=A+h,where h≡0 is an entire function with ρ（h）＜ρ（A）.Then g（k）+A1（z）g=0 does not have a solution g with λ（g）＜∞.