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本文研究亚纯系数的高阶线性微分方程,当方程系数满足一定条件时,得到方程的每一非零亚纯解具有无穷级且超级为n.此外,还研究了非齐次线性微分方程的亚纯解. 相似文献
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研究了非齐次线性微分方程f^{(k)}+A_{k-1}(z)f^{(k-1)}+...+A_{s}(z)f^{(s)}+...+A_{0}(z)f=F(z)
解的增长性,其中A_{j}(j=0,1,\cdots,k-1)及F是整函数. 在A_{s}比其他系数有较快增
长的情况下,得到了上述非齐次微分方程在一定条件下的超越整函数解的超级的精确估计. 相似文献
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《复变函数与椭圆型方程》2012,57(1):83-94
This article studies the problem on the fixed points and hyper-order of differential polynomials generated by solutions of two type of second order differential equations. Because of the control of differential equation, we can obtain some precise estimates of their hyper-order and fixed points. 相似文献
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关于高阶线性微分方程亚纯解的增长率 总被引:32,自引:0,他引:32
本文研究了二种类型的高阶线性齐次亚纯函数系数微分方程的亚纯解的增长性,当存在某个系数对方程的解的性质起主要支配作用时,我们对方程的亚纯解的增长率得到了精确的估计。 相似文献
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Zong Xuan Chen 《数学学报(英文版)》2002,18(1):79-88
In this paper, we investigate the growth of solutions of the second-order linear homogeneous differential equations with
entire coefficients of the same order, and obtain precise estimates of the hyper-order of their solutions.
Received November 15, 1999, Accepted May 10, 2000 相似文献
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二阶齐次与非齐次线性微分方程亚纯解的零点与增长性质估计(英文) 总被引:1,自引:1,他引:0
本文研究了方程f′′+A(z)f′+B(z)f=0与f′′+A(z)f′+B(z)f=F亚纯解的零点与增长性,其中A(z),B(z)(■0),F(z)(■0)为亚纯函数,得到了方程亚纯解的增长级、下级、超级、二级不同零点收敛指数等的精确估计,改进了KwonKi-Ho、陈宗煊与杨重骏、Benharrat Beladi等的结果. 相似文献
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Risto Korhonen 《Journal of Mathematical Analysis and Applications》2009,357(1):244-253
A version of the second main theorem of Nevanlinna theory is proved, where the ramification term is replaced by a term depending on a certain composition operator of a meromorphic function of small hyper-order. As a corollary of this result it is shown that if n∈N and three distinct values of a meromorphic function f of hyper-order less than 1/n2 have forward invariant pre-images with respect to a fixed branch of the algebraic function τ(z)=z+αn−1z1−1/n+?+α1z1/n+α0 with constant coefficients, then f○τ≡f. This is a generalization of Picard's theorem for meromorphic functions of small hyper-order, since the (empty) pre-images of the usual Picard exceptional values are special cases of forward invariant pre-images. 相似文献
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In this article, the growth of meromorphic solutions for a class of higher-order linear differential equation with meromorphic coefficients is investigated by applying the method of value distribution, and some estimates for the hyper-order of their solutions are obtained. 相似文献
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本文研究了与线性微分多项式有一个公共值的整函数.利用值分布和复震荡理论,获得了当整函数与其线性微分多项式有一个CM公共值时它们之间的关系,推广了已有的结果. 相似文献
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