高阶线性微分方程解与其小函数的增长性

Growth of Solutions of Higher Order Linear Differential Equations and Its Small Functions

利用整函数的Nevanlinna值分布理论和复微分方程的研究技巧,研究了高阶齐次线性微分方程解的增长性,探讨了高阶齐次线性微分方程解以及它们的一阶、二阶导数与小函数之间关系,得到了微分方程解以及它们的一阶、二阶导数与小函数零点的精确估计,推广和改进了一些文献中的结论.

The growth of solutions to higher order linear differential equations and its small functions was investigated using the Nevanlinna value distribution theory of entire functions and the investigation skills of complex differential equations.The relation between the 1st,2nd derivatives and the small functions was discussed,and precise estimate was obtained,which improved and generalized some results in literature.