具有缺项级数系数的非齐次线性微分方程解取小函数点的增长性

The Growth of Solutions of Certain Non-homogeneous Differential Linear Equations with Fabry Gap about Small Order of Growth Function

研究了高阶非齐次线性微分方程f(k)+Ak-1f(k-1)+…+A1f′+A0f=F的增长性问题,其中A0,A1,…,Ak-1,F是整函数.当存在系数A0为缺项级数且比其他系数有较快增长性时,得到了上述非齐次微分方程解的超级、解取小函数点的超级与方程系数的级3者之间的关系.

In this paper, the growth of solutions of the differential equation f^（k）＋Ak-1f^（k-1）＋…＋A1f^′＋A0f=F is investigated, where A0,A1,…,Ak-1,F are entire functions. The relationship among the hyper order of growth of the solution of equation, the hyper order of growth of solution to small order of growth function and the order of growth of coefficient of equation are obtained, when the dominant coefficient A0 has Fabry gap.