一类高阶代数微分方程代数体解的值分布

The value distribution of algebroid solutions of a type higher-order algebraic differential equations

利用亚纯函数或代数体函数的Nevanlinna值分布理论,研究了一类高阶代数微分方程的代数体解的值分布问题.证明了一类复高阶代数微分方程在存在代数体允许解并满足一适当条件的情况下,该方程的亏量问题.

Using Nevanlinna theory of the value distribution of meromorphic functions or algebroid functions, the problem of the value distribution of algebroid solutions of some algebraic differential equations is investigated. The deficient values of a type higher-order algebraic differential equations are obtained on condition that the equations exist admissible algebroid solutions and meet some proper conditions.