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]5769-05).
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
Download PDF Full-Text

Organizer:The Ministry of Education of China Sponsor:Fudan University Address:220 Handan Road, Fudan University, Shanghai, China E-mail:edcam@fudan.edu.cn
Designed by Beijing E-Tiller Co.,Ltd.