高阶非齐次线性微分方程解的性质

The Property of Solutions of a Class of Higher Order Nonhomogeneous Linear Differential Equations

摘要: 研究了非齐次线性微分方程~f^(k)+A_k-1f^(k-1)+\cdots+A_df^(d)+\cdots+A_0f=F~的解的增长性及零点,其中~A_j(j=0,1,\cdots,k-1)~为有限级整函数, F~为无穷级整函数,当存在~A_d(0 \leq d \leq k-1)~满足某些特殊条件时,~得到了上述非齐次线性微分方程解的性质.

Abstract: The growth of solutions for the equation f^(k)+A_k-1f^(k-1)+\cdots+A_df^(d)+\cdots+A_0f=F is investigated,where A_j(1,2,\cdots,k-1) are entire functions with finite order, F is an entire function with infinite order. ~If the coefficients A_d\; (0 \leq d \leq k-1) satisfy some certain conditions,~the properties of solutions for this equation are obtained.