勷勤数学•专家报告
题 目:Meromorphic Solutions to Higher Order Nonlinear Delay Differential Equations
报 告 人:李叶舟 教授 (邀请人:黄志波)
北京邮电大学
时 间:1月5日 11:00-12:00
地 点:数科院东楼401
报告人简介:
李叶舟,博士,北京邮电大学教授,博士研究生导师。从事复域微分方程理论,值分布理论和复动力系统的研究,主持国家自然科学基金4项。
摘 要:
Let $w(z)$ be non-rational meromorphic solutions with hyper-order less than 1 to a family of higher order nonlinear delay differential equations
$$ w(z + 1)w(z − 1) + a(z)\frac{w^{(k)} (z)}{w(z)}= R(z, w(z)), k \in \mathbb{N}^{+}, $$ where $a(z)$ is rational, $R(z, w(z)) = \frac{P (z,w(z))}{Q(z,w(z))} is an irreducible rational function in$ w$ with rational coefficients in $z$. This paper mainly show the relationships of the degree of $P(z, w(z))$ and $Q(z, w(z))$ when the above equations exist such solutions $w(z)$. There are also some examples to show that our results are sharp.
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