论文标题
关于海曼方程的先验仿药解决方案的注释
A note on the transcendental meromorphic solutions of Hayman's equation
论文作者
论文摘要
我们介绍了第二阶微分方程的先验性异常解的形式的完整描述\ begin {qore} \ tag†w'w'w'w'^2+a w'w+a w'w+b w^2 =α{w}+β{w}+β{w'}+γ+γ，\ deent e e e e e e exiptions，与Wiman-Valiron定理一起，我们的结果产生的结果是，任何先验的Meromororphic解决方案$ w $ of $（†）$都具有超订单$ς（w）\ leq n $，用于某些整数$ n \ geq 0 $。 Moreover, if $w$ has finite order $σ(w)=σ$, then $σ$ is in the set $\{n/2: n=1,2,\cdots\}$ and, if $w$ has infinite order and $γ\not\equiv0$, then the hyper-order $ς$ of $w$ is in the set $\{n: n = 1,2，\ cdots \} $。对于某些系数$ a，b，α，β，γ$，在这两组中的每个顺序或超顺序都可以实现。
We present a complete description of the form of transcendental meromorphic solutions of the second order differential equation \begin{equation}\tag† w''w-w'^2+a w'w+b w^2=α{w}+β{w'}+γ, \end{equation} where $a,b,α,β,γ$ are all rational functions. Together with the Wiman--Valiron theorem, our results yield that any transcendental meromorphic solution $w$ of $(†)$ has hyper-order $ς(w)\leq n$ for some integer $n\geq 0$. Moreover, if $w$ has finite order $σ(w)=σ$, then $σ$ is in the set $\{n/2: n=1,2,\cdots\}$ and, if $w$ has infinite order and $γ\not\equiv0$, then the hyper-order $ς$ of $w$ is in the set $\{n: n=1,2,\cdots\}$. Each order or hyper-order in these two sets is attained for some coefficients $a,b,α,β,γ$.
