| 一类具有缺项级数系数的高阶微分方程解的增长性 |
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| 引用本文： | 陈美茹,陈宗煊. 一类具有缺项级数系数的高阶微分方程解的增长性[J]. 华南师范大学学报(自然科学版), 2011, 0(4): 26-0 |
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| 作者姓名： | 陈美茹 陈宗煊 |
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| 作者单位： | 1.华南师范大学数学科学学院 |
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| 摘 要： | 研究了高阶非齐次微分方程f(k) +Ak-1f(k-1)+…+A1f1+Ao f=F,其中Ao,A1,…,F是整函数.当存在某个系 数Ad为缺项级数并对方程的解的性质起主要支配作用时,得到上述微分方程和对应的齐次微分方程在一定条件下超越解超级的精确估计.
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| 关 键 词： | Nevanlinna理论 微分方程 缺项级数 超级 |
| 收稿时间： | 2010-09-24 |
GROWTH OF SOLUTIONS OF A CLASS OF HIGHER- ORDER DIFFERENTIAL EQUATIONS WITH COEFFICIENTS HAVING FABRY GAP |
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| CHEN Meiru,CHEN Zongxuan. GROWTH OF SOLUTIONS OF A CLASS OF HIGHER- ORDER DIFFERENTIAL EQUATIONS WITH COEFFICIENTS HAVING FABRY GAP[J]. Journal of South China Normal University(Natural Science Edition), 2011, 0(4): 26-0 |
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| Authors: | CHEN Meiru CHEN Zongxuan |
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| Abstract: | This paper investigates the growth of solutions of a class of higher-order nonhomogeneous linear differential equation f^{(k)}+A_{k-1}f^{(k-1)}+...+A_{1}f'+A_{0}f=F and its homogeneous linear differential equation, where A_{0},A_{1},...A_{k-1},F are entire functions and the dominant coefficient A_{d} has fabry gap, we obtain general estimates of the growth and zeros of entire transcendtial solutions of higher order linear differential equations. |
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