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| Properties of Complex Oscillation of Solutions of a Class of Higher Order Linear Differential Equations |
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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： 888
Net amount： 782 |
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]5769-05). |
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| 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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