几类高阶非齐次微分方程解的增长性

研究了一类高阶非齐次微分方程 f ()k + A k -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 + h k -1()z eak -1z f ()k -1 +  + h1()z ea1z f ′+( 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.)

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

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.