线性微分多项式的值分布与线性微分方程的解增长(英文)

The value distribution of linear differential polynomials and the solution growth of linear differential equations

对线性微分多项式的值分布与线性奧分方程解的增长性进行了研究,并得到关于线性奧分多项式零点与极点的一个基本不等式.这一结果不仅蕴涵了Frank-Weissenborn不等式,而且揭示了线性微分多项式的值分布与线性微分方程解的增长性之间的一种联系.作为此结果的应用,Hayman-Yang不等式及几个著名的定理被推广.例子表明,文中所给定理的条件是基本的.

The value distribution of linear differential polynomials and the solution growth of linear differential equations are studied, and a fundamental inequality on the zeros and poles of linear differential polynomials has been obtained. This result not only covers Frank-Weissenbom inequality, and re- veals a relation between the value distribution of linear differential polynomials and the solution growth of linear differential equations. As its applications, Hayman-Yang inequality and some known theorems are generalized. The examples are provided to show that the conditions of theorems obtained in the present paper are essential.