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| 摘要: |
| 本文主要考察了非线性微分-差分方程
~ $ f(z)^{n}+a_{n-1}f(z)^{n-1}+\cdots+a_{1}f(z)+q(z)e^{Q(z)}f^{(k)}(z+c)=P(z)$ ~的有穷级非零整函数解的增长性和零点分布，其中~$q(z),~ Q(z),~P(z)$~是多项式,$q(z)\not\equiv 0,~Q(z)$~非常数;~$a_{i}(i=1,2,\cdots,n-1)\in\mathbb{C}$.~
特别地,~当~$n=2,~a_{1}\neq 0$~时,~我们得到了指数多项式解满足某些条件时,具有特别的形式,我们的结果推广了先前文献[9,10]的结果. |
| 关键词: 微分-差分方程 指数多项式 有穷级 |
| DOI： |
| 分类号:O174.5 O174.52 |
| 基金项目: |
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| SOLUTIONS OF NONLINEAR DIFFERENTIAL-DIFFERENCE EQUATIONS |
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zhangshimei
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| Abstract: |
| In this paper,~We consier the growth and distribution of zeros of entire solutions of finite order of nonlinear differential-difference equation
$$ f(z)^{n}+a_{n-1}f(z)^{n-1}+\cdots+a_{1}f(z)+q(z)e^{Q(z)}f^{(k)}(z+c)=P(z)$$
where~ $q(z), ~Q(z),~P(z)$ ~are polynomial and~ $n\geq2,~k\geq 1,~c\in\mathbb{C}\backslash\{0\},~a_{i}\in\mathbb{C}(1,2,\cdots,n-1)$.~Particularly,~when~$n=2$ ~and ~$a_{1} \neq 0 $The authors show that exponential polynomial solutions satisfying some condictions must reduce to rather specific forms,
this paper improves the results of [9,10] . |
| Key words: differential-difference equation exponential polynomial finite order. |
