线性微分方程亚纯解的零点和增长级的定量估计
Quantitative Estimations on Zeros and Growths of Meromorphic Solutions of Linear Differential Equations
摘要:
本文研究了高阶齐次和非齐次线性微分方程无穷极亚纯解的增长性问题，使方程的零点和增长性得到了精确估计。
Abstract:
In this paper, we investigate the growth of linear order meromorphic solution of higher order homogeneous and no-homogeneous linear differential equation, and we obtain some precise estimates for their zeros and hyper-orders.
参考文献
|
[1]
|
杨乐 (1982) 值分布论及其新研究. 科学出版社, 北京.
|
|
[2]
|
仪洪勋, 杨重骏 (1995) 亚纯函数唯一性理论. 科学出版社, 北京.
|
|
[3]
|
陈宗煊 (2000) 二阶复域微分方程解的不动点与超级. 数学物理学报, 3, 425-432.
|
|
[4]
|
Chen, Z.-X. and Yang, C.-C. (1999) Quantitative estimation on the zeros and growths of entire solutions of linear differential equations. Complex Variables, 42, 119-133.
|
|
[5]
|
廖莉, 陈宗煊 (2006) 关于超越亚纯系数微分方程亚纯解的超级. 江西师范大学学报(自然科学版), 1, 14-17.
|
|
[6]
|
Gundersen, G. (1988) Estimates for the logarithmic derivative of a meromorphic function, plus similar estimates. London Mathematical Society, 37, 88-104.
|
|
[7]
|
Hayman, W. (1974) The local growth of power series: A survey of the Wiman-Valiron method. Canadian Mathematical Bulletin, 17, 317-358.
|
|
[8]
|
He, Y.Z. and Xiao, X.Z. (1988) Algebroid functions and ordinary differential equations. Science Press, Beijing.
|
|
[9]
|
Valiron, G. (1949) Lectures on the general theory of integral functions. Chelsea, New York.
|
|
[10]
|
陈宗煊 (1996) 二阶亚纯系数微分方程亚纯解的零点. 数学物理学报, 3, 276-283.
|
|
[11]
|
Frank, G. and Hellerstein, S. (1986) On the meromorphic solution of non-homogeneous linear differential equations with polynomial coefficients. Proceedings London Mathematical Society, 53, 407-428.
|