| THE ZEROS AND ORDER OF MEROMORPHIC SOLUTIONS OF f^（k）＋Bf=H（z） |
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| 作者姓名： | Chen Zongxuan Yu Jiarong |
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| 作者单位： | CHEN ZONGXUAN;(Department of Mathematics，Jiangxi Normal University，Nanchang 330027，China.)YU JIARONG ;(Department of Mathematics，Wuhan University，Wuhan 430072，China.) |
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| 摘 要： | 1.IntroductionandResultsConsidernon-homogeneouslineardifferentialequationsoftheform1.Lameprovedin7]TheoremA.LetB(z),PO(z),PI(z)*06epolynomialssuchthatdegB=n21,degPO=p<(n k)/kandH=PI(z)epo('),then(a)IfdegPI
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| 关 键 词： | 线性微分方程 亚纯解 非齐次 多项式 |
| 收稿时间： | 1996/5/27 0:00:00 |
THE ZEROS AND ORDER OF MEROMORPHIC SOLUTIONS OF f^(k)+B*f=H(z) |
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| Chen Zongxuan,Yu Jiarong.THE ZEROS AND ORDER OF MEROMORPHIC SOLUTIONS OF f^(k)+B*f=H(z)[J].Chinese Annals of Mathematics,Series B,1998,19(4):433-444. |
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| Authors: | Chen Zongxuan and Yu Jiarong |
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| Institution: | [1]DepartmentofMathematics,JiangxiNormalUniversity,Nanchang330027,China [2]DepartmentofMathematics,WuhanUniversity,Wuhan430072,China |
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| Abstract: | Suppose that $B$ is a rational function having a pole at $\infty$ of order $n>0$ and that $H\nequiv 0$ is a meromorphic function satisfying $\si(H)=\be\not=(n+k)/k.$ If the differential equation $f^{(k)}+Bf=H(z)$ has a meromorphic solution $f$, then all meromorphic solutions $f$ satisfy
$$\bar{\la}(f)=\la(f)=\si(f)=\max\{\be, (n+k)/k\},$$ except at most one exceptional meromorphic solution $f_0.$ |
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| Keywords: | Linear differential equation Meromorphic solution Zero Order |
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