几类高阶非齐次微分方程解的增长性

Growth of Solutions of Several Classes of Higher Order Non-homogeneous Differential Equations

研究了一类高阶非齐次微分方程f(k)+Ak-1(z)f(k-1)++A0(z)f=Q(z),其中Aj(z)为有限级整函数,Q(z)为次数小于n的多项式,和另一类高阶非齐次微分方程f(k)+hk-1(z)eak-1zf(k-1)++h1(z)ea1zf′+(A1)(z)ebz+A2(z)edz f=Q(z),其中hj(z),Ai(z)为级小于1的整函数,Q(z)为次数小于n的多项式,在一定条件下,得到了方程解的级的精确估计。

In the paper, the authors investigate one class of higher order non-homogeneous differential equations f（k） ＋Ak-1（Z）f^（k-1） ＋……＋Ao（z）f= Q（z） , where Aj（z） are entire functions of finite order, Q（z） are polynomi- als with degQ〈n , and another class of higher order non-homogeneous differential equationsf^（k）＋hk-1（z）e^ah-1^zf^（k-1）＋……＋h1（z）e^a1zf＇＋（A1（z）e^bz＋A2（z）e^dx）f=Q（z） , where hj（z） , Ai（z） are entire func- tions, α（hj）〈 1 and α（Ai） 〈 1, Q（z） are polynomials with deg Q 〈n. Under certain conditions, the authors ob- tain some precise estimates of the order of solutions for those equations.