一类高阶线性微分方程解的增长性

利用 Nevanlinna 的基本理论和方法,研究了齐次线性微分方程() f k+A f k k??11++=及非齐次Af 0线性微分方程解的增长性.在假设存在某个(1 A s s k ?≤≤1)具有有限亏值的有限级整函数的情况下,证明了齐次线性微分方程的任一非零解均为无穷级,非齐次方程除1个例外解外,其它的非零解也均为无穷级

The Growth of Solutions for a Class Higher Order Linear Differential Equations

By using the fundamental theory and method of Nevanlinna,the growth of solutions of the homogeneous linear differential equation f(k)+Ak-1fk-1+…+Af= 0and non-homogeneous linear differential equation was inves-tigated.Assuming some As(1 ≤s≤k-1) is entire functions with a finite deficient value,it was proved that every so-lution f■0 of the homogeneous differential equation has infinite order.Furthermore,the solutions f■0 of non-homogeneous linear differential equation have the same property except for an extra solution.