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| THE ZEROS AND ORDER OF MEROMORPHIC SOLUTIONS OF f^(k)+B*f=H(z) |
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Citation： |
Chen Zongxuan,Yu Jiarong.THE ZEROS AND ORDER OF MEROMORPHIC SOLUTIONS OF f^(k)+B*f=H(z)[J].Chinese Annals of Mathematics B,1998,19(4):433~444 |
| Page view： 916
Net amount： 740 |
Authors： |
Chen Zongxuan; Yu Jiarong |
Foundation： |
the National Natural Science Foundation of 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 $f_0.$ |
Keywords： |
Linear differential equation,
Meromorphic solution, Zero,Order |
Classification： |
34A20, 30D35 |
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