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| 二阶微分方程解的零点分布 | |
| 引用本文： | 吴昭君,田宏根,吴佳.二阶微分方程解的零点分布[J].数学物理学报(A辑),2009,29(1):179-185. |
| 作者姓名： | 吴昭君 田宏根 吴佳 |
| 作者单位： | 吴昭君,Wu Zhaojun(成宁学院数学系,湖北咸宁,437100);田宏根,Tian Honggen(新疆师范大学数学系,乌鲁木齐,830054);吴佳,Wu Jia(成宁职业技术学院基础部,湖北成宁,437100) |
| 基金项目： | 国家自然科学基金，湖北省教育厅青年研究项目 |
| 摘 要： | 应用角域Nevanlinna理论和Ahlfors覆盖曲面理论, 研究了二阶微分方程f’’+A(z)f=0的解的零点分布. 证明了在复平面上至少存在一条半直线, 使得二阶微分方程解在该直线上的零点的径向收敛指数为无穷. 用新的方法证明了伍胜健在文献5]中的一个定理. |
| 关 键 词： | 零点收敛指数 复振荡 超级 Borel方向. |
| 收稿时间： | 2007-06-30 |
| 修稿时间： | 2008-10-21 |
On the Distribution of Zeros of Solutions of Second Order Differential Equations |
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| Wu Zhaojun,Tian Honggen,Wu Jia.On the Distribution of Zeros of Solutions of Second Order Differential Equations[J].Acta Mathematica Scientia,2009,29(1):179-185. | |
| Authors: | Wu Zhaojun Tian Honggen Wu Jia |
| Institution: | (1.Department of Mathematics, Xianning College, Hubei Xianning 437100; 2.Department of Mathematics, Xingjiang Normal University, Wulumuqi 830054; 3.Department of Basic, Xianning Technology College, Hubei Xianning 437100) |
| Abstract: | In this paper, we investigate the distribution of zeros of solutions of second order differential equations f’’+A(z)f=0, where A(z) is an entire function of finite order. By using the Nevanlinna’s characteristic function and Ahlfors-Shimizu’s characteristic function on an angular domain, we established the existence of some ray which has the property that near which the exponent of convergence of the zero-sequence is infinite. Furthermore, by using a new method, we give a different proof of the Theorem 2 which has been given by Wu Shengjian in 5]. |
| Keywords: | The exponent of convergence of the zero-sequencezz Complex oscillationzz Hyper orderzz Borel direction zz |
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