复高阶微分方程的解

Solutions of Complex Higher-Order Differential Equations

利用亚纯函数的Nevanlinna值分布理论以及最大模原理,讨论了一类复高阶微分方程的代数体解以及一类复高阶微分方程组的超越亚纯解的存在性问题,得到了两个结论.还推广了一些文献的结论,例子表明该文的结论是精确的.

Using Nevanlinna theory of the value distribution of meromorphic functions, and maximum modulus principle, we investigate the problem of the existence of the algebroid solutions of a class of complex higher-order differential equations and the transcendental meromorphic solutions of a class of system of complex higher-order differential equations and obtain two results. Extensions of some results in references are presented. Examples show that our results are precise.