一类高阶非齐次线性微分方程亚纯解的零点

利用亚纯函数的值分布理论研究了下列高阶线性微分方程解的增长性及解的零点增长性,f^((k))+A_(k-1)f((k))+A_(k-1)f^((k-1))+…+A_1f′+A_0f=F(z)其中A_0,A_1,…,A_(k-1),F≠0是亚纯函数.证明了如果A_0以∞为亏值或Borel例外值,那么方程的所有非零解的零点收敛指数均为无穷,至多除去一个例外解,获得的结果推广了以前一些文献的结论.

The Zero of Meromorphic Solutions of a Class of Higher Order Nonhomogeneous Linear Differential Equation

Using theory of the value distribution of meromorphic functions,the problem of the growth and zero of solutions of f~((k))+A_(k-1)f~((k-1))+…+A_1f'+A_0f = F(z) is investigated, where A_0,A_1,…,A_(k-1) and F(?)0 are meromorphic functions.And under the assumption of certain proper conditions of A_0(z),∞is a deficient value or Borel exceptional value of A_0, we prove a result which the exponents of convergence of the zero-sequence of every nontrivial solutions f(z) of the equation is of infinite,up to remove an exception solution,and improve some results in previous references.