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