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 withρ(A)〈1/2.Suppose that k≥2 and f(k)+A(z)f=0 has a solution f withλ(f)〈ρ(A),and suppose that A1=A+h,where h≡0 is an entire function withρ(h)〈ρ(A).Then g(k)+A1(z)g=0 does not have a solution g withλ(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 withρ(A)〈1/2.Suppose that k≥2 and f(k)+A(z)f=0 has a solution f withλ(f)〈ρ(A),and suppose that A1=A+h,where h≡0 is an entire function withρ(h)〈ρ(A).Then g(k)+A1(z)g=0 does not have a solution g withλ(g)〈∞.
