【摘要】 利用亚纯函数的Nevanlinna值分布理论和最大模原理,讨论了如下二阶代数微分方程组存在超越亚纯解时,该解的多项式的零点问题,{（w″₁）ⁿ=P₁（z,w₂）/Q₁（z,w₂） （w″₂）ⁿ=P₂（z,w₁）/Q₂（z,w₁）得到2个结果。结果表明如果该类二阶代数微分方程组存在超越亚纯解（w₁（z）,w₂（z））时,且V₁（z,w₂）与V₂（z,w₁）分别为Q₁（z,w₂）与Q₂（z,w₁）或P₁（z,w₂）与P₂（z,w₁）的质因子,则V₁（z）=V₁（z,w₂）与V₂（z）=V₂（z,w₁）中至少有一个具有无穷多个零点。该结果推广了一阶复微分方程的结论。更多还原

【Abstract】 Based on the distribution of Nevanlinna value of meromorphic functions and maximum modulus principle,the zero problems of polynomials is discussed if the following second-order algebraic differential equations exist beyond the meromorphic solutions.{（w″₁）ⁿ=P₁（z,w₂）/Q₁（z,w₂） （w″₂）ⁿ=P₂（z,w₁）/Q₂（z,w₁）The obtained two results show if the second-order algebraic differential equations of this class have prime factors beyond meromorphic solutions（w₁（z）,w₂（z））,and V₁（z,w₂）and V₂（z,w₁）are Q₁（z,w₂）and Q₂（z,w₁）or P₁（z,w₂）and P₂（z,w₁）,respectively,then V₁（z）=V₁（z,w₂）,and V₂（z）=V₂（z,w₁）,at least one of them has an infinite number of zeros.The presented results generalize the conclusion of the first-order complex differential equations.更多还原