On Complex Oscillation Theory of Solutions of Some Higher Order Linear Differential Equations 
Received:November 27, 2011 Revised:March 27, 2012 
Key Word:
complex differential equations entire function the growth of order the exponent of convergence of the zeros.

Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant No.11171080) and Foundation of Science and Technology Department of Guizhou Province (Grant No.[2010] 07). 

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Abstract: 
In this paper, we shall use Nevanlinna theory of meromorphic functions to investigate the complex oscillation theory of solutions of some higher order linear differential equation. Suppose that $A$ is a transcendental entire function with $\rho(A)<\frac{1}{2}$. Suppose that $k\geq 2$ and $f^{(k)}+A(z)f=0$ has a solution $f$ with $\lambda(f)<\rho(A)$, and suppose that $A_{1}=A+h$, where $h\not\equiv 0$ is an entire function with $\rho(h)<\rho(A)$. Then $g^{(k)}+A_{1}(z)g=0$ does not have a solution $g$ with $\lambda(g)<\infty$. 
Citation: 
DOI:10.3770/j.issn:20952651.2012.04.006 
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