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 ent...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）〈∞.展开更多
基金Supported by the National Natural Science Foundation of China (Grant No. 11171080)Foundation of Scienceand Technology Department of Guizhou Province (Grant No. [2010] 07)
文摘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）〈∞.
