关于线性微分方程的解的性质

doi:10.12677/pm.2012.22015

期刊菜单

关于线性微分方程的解的性质
The Relation between Solutions of a Class of Higher Order Differential Equations with Periodic Coefficients and Functions of Small Growth

DOI: 10.12677/pm.2012.22015, PDF, HTML, 国家自然科学基金支持
作者: 王青：华南师范大学数学科学学院；陈宗煊：
关键词: 微分方程；整函数；小函数；收敛指数；Differential Equation; Entire Functions; Function of Small Growth; Exponent of Convergence

摘要: 在文中研究了微分方程 $f ^{(k)}+[P_{k-1}(e^{z})+Q_{k-1}(e^{-z})]f^{(k-1)}+ \cdot \cdot \cdot +[P_0(e^{z})+Q_0(e^{-z})]f = R_1(e^z)+R_2}(e^{-z})$ 和 $f ^{(k)}+[P_{k-1}(e^{z})+Q_{k-1}(e^{-z})]f^{(k-1)}+ \cdot \cdot \cdot +[P_0(e^{z})+Q_0(e^{-z})]f = 0$ 的解以及它们的一阶导数与小函数的关系。

Abstract: In this paper, we investigate the differential equations $f ^{(k)}+[P_{k-1}(e^{z})+Q_{k-1}(e^{-z})]f^{(k-1)}+ \cdot \cdot \cdot +[P_0(e^{z})+Q_0(e^{-z})]f = 0$ and $f ^{(k)}+[P_{k-1}(e^{z})+Q_{k-1}(e^{-z})]f^{(k-1)}+ \cdot \cdot \cdot +[P_0(e^{z})+Q_0(e^{-z})]f = R_1(e^z)+R_2}(e^{-z})$ . Moreover, we obtained the relation between solutions of the two differential equations and their 1th derivatives of differential equa-tion and small functions.

文章引用：王青, 陈宗煊. 关于线性微分方程的解的性质[J]. 理论数学, 2012, 2(2): 88-96. http://dx.doi.org/10.12677/pm.2012.22015

参考文献

[1]	杨乐. 值分布论及其新研究[M]. 北京: 科学出版社, 1982.
[2]	陈宗煊. 二阶复域微分方程解的不动点与超级[J]. 数学物理学报, 2000, 20(3): 425-432.
[3]	Z. X. Chen, S. Kwangho. Subnormal solutions of differential equations with periodic coefficients. Acta Mathematica Scientia, 2010, 30B(1): 75-88.
[4]	徐俊峰, 仪洪勋. 微分方程的解和小函数的关系[J]. 数学学报, 2010, 53(2): 85-90.

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