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Let $A(z)$ be an entire function with $\mu(A)<\frac{1}{2}$ such that the equation $f^{(k)}+A(z)f=0$, where $k\geq 2$, has a solution $f$ with $\lambda(f)<\mu(A)$, and suppose that $A_{1}=A+h$, where $h\not\equiv 0$ is an entire function with $\rho(h)<\mu(A)$. Then $g^{(k)}+A_{1}(z)g=0$ does not have a solution $g$ with $\lambda(g)<\infty$.  相似文献
2.
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)<∞.  相似文献
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