RADIAL OSCILLATION OF LINEAR DIFFERENTIAL EQUATION
RADIAL OSCILLATION OF LINEAR DIFFERENTIAL EQUATION
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DOI：
10.4134/bkms.2012.49.5.911
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发表时间：
2012-09
影响因子：
0.5
通讯作者：
Zhaojun Wu
中科院分区：
文献类型：
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作者：
Zhaojun Wu
抽象的。研究了具有超越整函数的高阶齐次线性微分方程解f(K)+An−2(Z)f(k−2)+···+A1(Z)f‘+A0(Z)f=0的径向振动性.所得结果推广了[Z.Wu，D.Sun，高阶线性微分方程解的角分布，J.Korea Math.Soc]中的某些结果。44(2007)，第6号，1329-1338号]。1.引言和主要结果在本文中，亚纯函数总是指在整个复平面C上是亚纯的函数。假设亚纯函数的基本Defi数列、定理和标准符号是已知的(见[11]、[22]或[24])。自从1982年Bankand Laine[1]的文章发表在Trans上以来，已经出现了许多从ff理论的观点来研究复微分方程组整体理论的论文。阿默。数学课。SoC。我们请读者参考莱恩[12]和高等人的书[6]。关于(1)f解的径向振动理论的fi第一一般性研究
Abstract. In this paper, the radial oscillation of the solutions of higherorder homogeneous linear differential equationf (k) + A n−2 (z)f (k−2) + ···+ A 1 (z)f ′ + A 0 (z)f = 0with transcendental entire function coefficients is studied. Results are ob-tained to extend some results in [Z. Wu and D. Sun, Angular distributionof solutions of higher order linear differential equations, J. Korean Math.Soc. 44(2007), no. 6, 1329–1338]. 1. Introduction and main resultsIn this paper, the meromorphic function always means a function beingmeromorphic in the whole complex plane C. Assume that the basic definitions,theorems and standard notations of the Nevanlinna theory for meromorphicfunction (see [11], [22] or [24]) are known. There have appeared many paperson the global theory of complex differential equations which were studied fromthe point of view of Nevanlinna theory, since 1982 when the article by Bankand Laine [1] appeared in Trans. Amer. Math. Soc. We refer the reader tothe books by Laine [12], and by Gao etc. [6]. The first general research on theradial oscillation theory of the solutions of(1) f