2阶微分方程的解与小函数的关系

The Relations between Solutions of Second Order Linear Differential Equations with Functions of Small Growth

运用Nevanlinna值分布的基本理论和方法,研究了几类2阶线性微分方程的解及其导数取小函数的不同点的收敛指数,得到了方程解及其导数取小函数的不同点的收敛指数为无穷和2阶收敛指数等于解的超级的精确结果.

It was investigated that the relations between solutions of second order linear differential equations and their 1 th and 2 th derivatives with the small growth functions by using the theory and the method of Nevanlinna val-ue distribution. The precision result was obtained that convergence exponents of various points of equation solutions and their derivatives fetch the small growth function is infinite and the 2 th convergence exponents with the hyper or-der of solution is equal.