| 高阶齐次线性微分方程解的零点 |
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| 引用本文： | 蓝双婷,陈宗煊.高阶齐次线性微分方程解的零点[J].数学学报,2012(3):525-534. |
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| 作者姓名： | 蓝双婷 陈宗煊 |
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| 作者单位： | 华南师范大学数学科学学院 |
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| 基金项目： | 国家自然科学基金资助项目(11171119) |
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| 摘 要： | 研究了一类高阶齐次线性微分方程解的零点收敛指数,并得到当方程的系数A_0为整函数,其泰勒展式为缺项级数,并且A_0起控制作用时,方程f~((k))+A_(k-2)f~((k-2))+…+A_1f′+A_0f=0的任意两个线性无关解f_1,f_2满足max{λ(f_1),λ(f_2)}=∞,其中λ(f)表示亚纯函数.f的零点收敛指数.
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| 关 键 词： | 微分方程 零点收敛指数 缺项级数 |
Zeros of Solutions of Higher Order Homogeneous Linear Differential Equations |
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| Shuang Ting LAN Zong,Xuan CHEN.Zeros of Solutions of Higher Order Homogeneous Linear Differential Equations[J].Acta Mathematica Sinica,2012(3):525-534. |
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| Authors: | Shuang Ting LAN Zong Xuan CHEN |
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| Affiliation: | School of Mathematical Sciences,South China Normal University, Guangzhou 510631,P.R.China |
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| Abstract: | We investigate the exponent of convergence of zeros of solutions for some higher order homogeneous linear differential equation.When A0 is an entire function that its taylor expansion is a gap power series and A0 is the dominant coefficient,we proved that any two linearly independent solutions f1 and f2 of equation satisfy max{A（f1）,λ（f2）} =∞,whereλ（f） denotes the exponent of convergence of zeros of meromorphic function f. |
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| Keywords: | differential equation exponent of convergence of zeros gap power series |
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