一类Riccati微分方程亚纯解的性质
Properties of a Class of Meromorphic Solutions of Differential Riccati Equations
摘要:
对系数均为有理函数的Riccati微分方程,我们在某些特殊条件下,给出了其亚纯解的增长级,极点收敛指数,零点收敛指数和不动点收敛指数的精确估计。
Abstract: For the meromorphic solution of differential Riccati equations whose coefficients are all rational functions, we give sharp estimates of the order of growth of it, and the exponents of convergence of the zeros, poles and fixed points of it for certain special cases.
参考文献
[1]
|
W. Hayman. Meromorphic functions. Oxford: Clarendon Press, 1964.
|
[2]
|
I. Laine. Nevanlinna theory and complex differential equations. Berlin: W.de Gruyter, 1993.
|
[3]
|
杨乐. 值分布论及其新研究[M]. 北京: 科学出版社, 1982.
|
[4]
|
G. Gundersen. Estimates for the logarithmic derivative of a meromorphic function, plus similar estimates. Journal of The London Mathematical Society-Second Series,1988, 37(2): 88-104.
|
[5]
|
Z.-X. Chen, C.-C. Yang. Some oscillation theorems for linear differential equations with meromorphic coefficients. Southeast Asian Bulletin of Mathematics, 1999, 23: 409-417.
|
[6]
|
S. Bank, J. Langley. On the oscillation theory of where is entire. Transactions of the American Mathematical Society, 1982, 273: 351-363.
|