高阶非线性代数微分方程组的亚纯允许解

Meromorphic admissible solution of systems governed by higher order non-linear algebraic differential equations

利用亚纯函数的Nevanlinna值分布理论,研究了高阶非线性代数微分方程组亚纯允许解的存在性问题,获得了微分方程组的亚纯解或同为允许的,或同为非允许的,进而得到了更一般的结果.

Using Nevanlinna theory of the value distribution of meromorphic functions,the problem of the existence of meromorphic admissible solutions of complex higher-order nonlinear algebraic differential equation is investigated. It is obtained that the meromorphic solution of the differential equations system are all admissible or non admissible. Moreover, some other results are also given, which are more general than the previous ones.