一类高阶线性微分方程解的超级估计

利用Nevanlinna的值分布理论和分类讨论的思想方法,研究了一类高阶齐次线性微分方程〖WTBX〗f(k)+H_k-1f(k-1)++H1f+H0f=0解的增长性，得到了一些有意义的结果：当Hj(z) (j=0,1,,k-1)是整函数时, 根据线性微分方程的一般理论, 上述方程的每个解都是整函数. 当方程系数满足: Hj(z)=hj(z)ePj(z)〖KG0.8mm〗(j=0,1,,k-1), Pj(z)是首项系数为aj的n〖KG0.5mm〗(n1)次多项式, hj(z)为整函数,(hj(z))s, as=dsei, al=-dlei, ds0, dl0. 对 js,l, aj=djei〖KG0.8mm〗(dj0)或aj=-djei, max{dj;js,l}=d

Estimate of the Hyper-Order of Solutions for Certain Higher Order Linear Differential Equations

By utilizing Nevanlinna's value distribution theory of meromorphic functions and categorized discussion method, the growth of solutions of higher order differential equations is investigated and some important results are obtained.When Hj(z) (j=0,1,,k-1) are entire functions, according to the general theory of linear differential equations, every solution of the above equations with entire coefficients is entire function. When the coefficients of the above equations satisfy: Hj(z)=hj(z)ePj(z)(j=0,1,,k-1),Pj(z) are 〖JP2〗polynomials with degree n and leading coefficients aj, hj(z) are entire functions, (hj(z))s, as=dsei,〖JP〗 al=-dlei, ds0, dl0. For js,l, aj=djei(dj0) or aj=-djei, max{dj;js,l}=d