亚纯函数系数的高阶微分方程的解与其小函数的增长性  

The Growth of Solutions of Meromorphic Funtion Coefficients of Higher Order Differential Equations with Functions of Small Growth

作　　者：金瑾[1] 

机构地区：[1]贵州省毕节学院数学系,贵州毕节551700

出　　处：《山西大同大学学报（自然科学版）》2012年第3期1-4,共4页Journal of Shanxi Datong University(Natural Science Edition)

基　　金：贵州省科学技术基金资助项目[2010GZ43286];贵州省科学技术基金项目[2012GZ10526];贵州省毕节地区科研基金资助项目[2011-02]

摘　　要：研究了高阶线性齐次微分方程f(k)+Ak-(1z)f(k-1)+…+A(1z)f'+A(0z)eazf=0解的增长性,其中,A(jz)堍0是亚纯函数,σ(A)j<1(j=0,1,2,…,k-1),a为非零复常数,得到了方程解的一阶导数、二阶导数、微分多项式与小函数之间的关系。In this paper, the growth of solutions of homogeneous higher order linear Differential equation is investigated, f（k）＋Ak-1（z）f^（k-1）＋…＋A1（z）f′＋A0（z）e^azf=0 in the Aj （z）≠0 were meromorphic functions, δ （Aj）〈1 （j=0, 1, 2…, k-1）, a is non-zero constant. Obtains their 1st,2st derivatives, differential polynomial of differential equations with function of small growth.

关 键 词：线性微分方程 小函数 亚纯函数 收敛指数 

分 类 号：O174.5[理学—数学]