| 关于二阶线性微分方程解的增长性 |
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| 引用本文： | 宫娟,陈宗煊.关于二阶线性微分方程解的增长性[J].华南师范大学学报(自然科学版),2012,44(1):29-0. |
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| 作者姓名： | 宫娟 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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| 基金项目： | 国家自然科学基金项目(10871076) |
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| 摘 要： | 研究了二阶微分方程~$f'+A_{1}(z)P(e^z)f'+A_{0}(z)Q(e^z)f=0$~和~$f'+(A_{1}(z)P(e^z)+D_{1}(z))f'\\+(A_{0}(z)Q(e^z)+D_{0}(z))f=0$~ 解的增长性，其中~$P(e^z)$~与~$Q(e^z)$~是~$e^z$~的非常数多项式，它们的常数项\\都为零，且次数不相等.~证明了该方程的每个非零解有无穷级.
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| 关 键 词： | 微分方程 整函数 增长级 |
| 收稿时间： | 2010-12-07 |
On the Growth of Solutions of Second Order Linear Differential Equations |
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| GONG Juan,CHEN Zongxuan.On the Growth of Solutions of Second Order Linear Differential Equations[J].Journal of South China Normal University(Natural Science Edition),2012,44(1):29-0. |
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| Authors: | GONG Juan CHEN Zongxuan |
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| Institution: | (School of Mathematics,South China Normal University,Guangzhou 510631,China) |
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| Abstract: | The growth of solutions of the differential equations f ″+A1(z)P(ez)f ′+A0(z)Q(ez)f=0 and f ″+(A1P(ez)+D1(z))f ′+(A0Q(ez)+D0(z))f=0 is investigated,where P(ez)and Q(ez)are nonconstant polynomials without constant term,and deg P is not equal to deg Q.It is showed that the order of growth of each nonzero solution of the above equations is infinite. |
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| Keywords: | differential equation entire function order of growth |
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