| Some Properties of Solutions of Periodic Second Order Linear Differential Equations |
| Received:March 01, 2009 Revised:October 14, 2009 |
| Key Words:
periodic differential equation complex oscillation regular order of growth.
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.10871076) and the Startup Foundation for Doctors of Jiangxi Normal University (Grant No.2614). |
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| Abstract: |
| In this paper, the zeros of solutions of periodic second order linear differential equation $y'' Ay=0$, where $A(z)=B(e^z)$, $B(\zeta)=g(\zeta) \sum_{j=1}^pb_{-j}\zeta^{-j}$, $g(\zeta)$ is a transcendental entire function of lower order no more than $1/2$, and $p$ is an odd positive integer, are studied. It is shown that every non-trivial solution of above equation satisfies the exponent of convergence of zeros equals to infinity. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2011.02.011 |
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