应用角域Nevanlinna理论和Ahlfors覆盖曲面理论,研究了二阶微分方程f″+A(z)f=0的解的零点分布.证明了在复平面上至少存在一条半直线,使得二阶微分方程解在该直线上的零点的径向收敛指数为无穷.用新的方法证明了伍胜健在文献[5]中的一个定理.
In this paper, we investigate the distribution of zeros of solutions of second order differential equations f″ + A(z)f = 0, where A(z) is an entire function of finite order. By using the Nevanlinna's characteristic function and Ahlfors-Shimizu's characteristic function on an angular domain, we established the existence of some ray which has the property that near which the exponent of convergence of the zero-sequence is infinite. Furthermore, by using a new method, we give a different proof of the Theorem 2 which has been given by Wu Shengjian in [5].