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| 摘要: |
| 本文研究了线性微分方程f(n) + An-1f(n-1) + … + A1f' + A0f = 0 亚纯解的动力学性质, 其中n ≥ 2,Ai(z)(i = 0, 1,… , n-1) 是具有有限下级的亚纯函数. 利用亚纯函数的Nevanlinna 值分布理论, 获得了一定条件下方程亚纯解的Julia 集的径向分布的下界, 推广了相关文献的结果. |
| 关键词: 微分方程 亚纯解 Julia集 径向分布 |
| DOI： |
| 分类号:O174.52 |
| 基金项目:国家自然科学基金(11001057);苏州科技学院科研基金项目(XKQ201405). |
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| RADIAL DISTRIBUTIONS OF JULIA SETS OF MEROMORPHIC SOLUTIONS OF LINEAR DIFFERENTIAL EQUATIONS |
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SUN Gui-rong,HUANG Zhi-gang
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| Abstract: |
| This paper is devoted to studying the dynamical properties of solutions of f(n) + An-1f(n-1) + … + A0(z)f = 0, where n(≥ 2) is an integer, and Ai(z)(i = 0, 1,… , n-1) are meromorphic functions of finite lower order. By using Nevanlinna theory of the value distribution of meromorphic functions, we obtain the lower bound on the radial distribution of Julia sets of solutions of such equations in some additional conditions, which improves some results of concerned literature. |
| Key words: differential equation meromorphic function Julia set radial distribution |
