Properties of Complex Oscillation of Solutions of a Class of Higher Order Linear Differential Equations |
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Authors: | Jianren LONG and Yezhou LI |
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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. |
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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
$\lambda(g)<\infty$. |
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Keywords: | Complex differential equations Entire function Order of growth & Exponent of convergence of the zeros |
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