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| 摘要: |
| 本文研究一类整函数系数高阶齐次线性微分方程解的零点分布. 利用Nevanlinna 值分布理论, 得到当系数Ak-1的增长性起主要支配作用时, 方程f(k) + Ak-1f(k-1) + … + A0f =0 任意超越解的零点收敛指数为无穷, 推广了Langley 和Bank 等人的结果. |
| 关键词: 整函数 微分方程 增长级 零点收敛指数 |
| DOI： |
| 分类号:O174.5 |
| 基金项目:国家自然科学基金资助项目(11201195);江西省自然科学基金项目(20122BAB201012;20132BAB201008). |
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| ZEROS OF SOLUTIONS OF CERTAIN HIGHER ORDER HOMOGENEOUS LINEAR DIFFERENTIAL EQUATIONS |
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ZENG Juan-juan,LIU Hui-fang
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| Abstract: |
| In this paper, we investigate the distribution of the zeros of the solutions for certain higher order homogeneous linear differential equationsf(k) + Ak-1f(k-1) + … + A0f = 0 with entire coefficients. By using the Nevanlinna's value distribution theory, we obtain that the exponent of convergence of zeros of every transcendental solution is infinite when Ak-1 is the dominant coefficient, which extends the results of Langley and Bank. |
| Key words: entire function differential equation growth of order exponent of convergence of zeros |
