一类整函数系数微分方程解的复振荡

The Complex Oscillation of a Class of Linear Differential Equation with Entire Coefficients

中文关键词:  微分方程  整函数  增长级  零点  收敛指数.

英文关键词:linear differential equation  entire functions  order  zero  exponent of convergence.

中文摘要:

      本文研究了微分方程~$f^{(k)}+A_{k-1}f^{(k-1)}+\cdots+A_0f=F\ (k\ge2)$ 解的增长级和零点收敛指数, 其中~$A_j=B_je^{P_j},j=0,1,\cdots,k-1,B_j(z)$ 为整函数,$P_j(z)$ 为多项式,$\sigma(B_j)<{\rm deg}P_j$.

英文摘要:

      This paper deals with the orders and zeros of the solutions of the differential equation $$f^{(k)}+A_{k-1}f^{(k-1)}+\cdots+A_0f=F, k\ge2,$$ where $A_j=B_je^{P_j},j=0,1,\cdots,k-1,B_j(z)$ are entire functions, $P_j(z)$ are polynomials, and $\sigma(B_j)<{\rm deg}P_j$.