复微分方程组的超越解

Transcendental Solutions of Systems of Complex Differential Equations

利用最大模原理,讨论了复代数微分方程组的超越亚纯解存在性问题,得到了在一定条件下,该方程组的超越解为代数解的一个结果.例子表明这个结果是精确的.

Using maximum modulus principle,we investigate the problem of the existence of the transcendental meromorphic solutions of system of complex algebraic differential equations,and obtain a result which the system only the algebraic solution under certain conditions.Examples show that our results are sharp.