外文翻译--一些周期性的二阶线性微分方程解的方法

《外文翻译--一些周期性的二阶线性微分方程解的方法》由会员分享，可在线阅读，更多相关《外文翻译--一些周期性的二阶线性微分方程解的方法（12页珍藏版）》请在毕设资料网上搜索。

1、 滨 州 学 院 外 文 翻 译 学号： 2009010477 姓名： 曲洋 Some Properties of Solutions of Periodic Second Order Linear Differential Equations 1. Introduction and main results In this paper, we shall assume that the reader is familiar with the fundamental results and the stardard notations of the Nevanlinnas value dist

2、ribution theory of meromorphic functions 12, 14, 16. In addition, we will use the notation )(f ， )(f and )(f to denote respectively the order of growth, the lower order of growth and the exponent of convergence of the zeros of a meromorphic function f ， )(fe （ see 8）， the e-type order of f(z), is de

3、fined to be r frTf re ),(loglim)( Similarly, )(fe ， the e-type exponent of convergence of the zeros of meromorphic function f , is defined to be r frNf re )/1,(lo glim)( We say that )(zf has regular order of growth if a meromorphic function )(zf satisfies r frTf r lo g ),(lo glim)( We consider the s

4、econd order linear differential equation 0 Aff Where )()( zeBzA is a periodic entire function with period /2 i . The complex oscillation theory of (1.1) was first investigated by Bank and Laine 6. Studies concerning (1.1) have een carried on and various oscillation theorems have been obtained 211, 1

5、3, 1719. When )(zA is rational in ze ， Bank and Laine 6 proved the following theorem Theorem A Let )()( zeBzA be a periodic entire function with period /2 i and rational in ze .If )(B has poles of odd order at both and 0 , then for every solution )0)( zf of (1.1), )( f Bank 5 generalized this result: The above conclusion still holds if we just suppose that both and 0 are poles of )(B , and at least one is of odd order. In addition, the