
 
Properties of Complex Oscillation of Solutions of a Class of Higher Order Linear Differential Equations 
 
Citation： 
Jianren LONG,Yezhou LI.Properties of Complex Oscillation of Solutions of a Class of Higher Order Linear Differential Equations[J].Chinese Annals of Mathematics B,2020,41(1):27~36 
Page view： 45
Net amount： 46 
Authors： 
Jianren LONG; Yezhou LI 
Foundation： 
This work was supported by the National Natural Science
Foundation of China (Nos.11571049, 11501142, 11861023) and the
Foundation of Science and Technology project of Guizhou Province of
China (No.[2018]576905). 


Abstract： 
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
$\lambda(g)<\infty$. 
Keywords： 
Complex differential equations, Entire function, Order of growth,& Exponent of convergence of the zeros 
Classification： 
34M10, 30D35 

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