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Properties of Complex Oscillation of Solutions of a Class of Higher Order Linear Differential Equations
Authors:Jianren  LONG and Yezhou  LI
Institution:School of Computer Science and School of Science, BeijingUniversity of Posts and Telecommunications, Beijing 100876, China; School of Mathematical Science, Guizhou Normal University, Guiyang 550001, China. and Corresponding author. School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China.
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
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