【摘要】 运用Nevanlinna值分布的理论和方法,研究了微分方程f(k)+Ak-1f(k-1)+…+A1f’+A0f=0(k≥2)解的增长性,其中Aj(j=0,1,…,k-1)是亚纯函数,通过给定Aj的不同条件,证明了齐次线性微分方程的任一非零解均为无穷级.更多还原

【Abstract】 The growth of solutions of the differential equation f(k)+ … + A0 f = 0(k ≥2) is investigated by using the fundamental theory of Nevanlinna value distribution,where Aj(0 ≤ j ≤ k-1) are meromorphic functions.It is proved that every nontrivial solution f of the equation is of infinite order with giving some different condition on Aj(0 ≤j ≤ k-1).更多还原