| 一类高阶线性微分方程解的复振荡 |
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| 引用本文： | 龙见仁. 一类高阶线性微分方程解的复振荡[J]. 数学研究及应用, 2012, 32(4): 423-430 |
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| 作者姓名： | 龙见仁 |
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| 作者单位： | 贵州师范大学数学与计算机科学学院, 贵州 贵阳 550001; 中国科学院数学与系统科学研究院, 北京 100190 |
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| 基金项目： | 国家自然科学基金(Grant No.11171080),贵州省科学技术基金(Grant No.[2010] 07). |
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| 摘 要： | 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 ρ(A)<1/2.Suppose that k≥2 and f(k)+A(z)f=0 has a solution f with λ(f)<ρ(A),and suppose that A1=A+h,where h≡0 is an entire function with ρ(h)<ρ(A).Then g(k)+A1(z)g=0 does not have a solution g with λ(g)<∞.
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| 关 键 词： | complex differential equations entire function the growth of order the exponent of convergence of the zeros. |
| 收稿时间： | 2011-11-27 |
| 修稿时间： | 2012-03-27 |
On Complex Oscillation Theory of Solutions of Some Higher Order Linear Differential Equations |
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| Jianren LONG. On Complex Oscillation Theory of Solutions of Some Higher Order Linear Differential Equations[J]. Journal of Mathematical Research with Applications, 2012, 32(4): 423-430 |
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| Authors: | Jianren LONG |
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| Affiliation: | School of Mathematics and Computer Science, Guizhou Normal University, Guizhou 550001, P. R. China; Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, P. R. China |
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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)
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| Keywords: | complex differential equations entire function the growth of order the exponent of convergence of the zeros. |
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