一类高阶线性微分方程解的复振荡性质  

ON THE PROPERTIES OF COMPLEX OSCILLATION OF THE SOLUTIONS OF A TYPE OF HIGHER ORDER LINEAR DIFFERENTIAL EQUATIONS

作　　者：曹廷彬[1] 陈宗煊[2] 涂金[3] 郑秀敏[3] 

机构地区：[1]南昌大学数学系,江西南昌330031 [2]华南师范大学数学系,广东广州510631 [3]江西师范大学数学系,江西南昌330022

出　　处：《数学杂志》2008年第1期31-38,共8页Journal of Mathematics

基　　金：国家自然科学基金资助项目(10771121);高校博士点专项科研基金(20060422049)

摘　　要：本文研究一类高阶线性齐次与非齐次迭代级整函数系数微分方程解的增长性问题.当存在某个系数或自由项对方程解的性质起主要支配作用时,得到了方程解的迭代级及其零点的迭代收敛指数的精确估计,推广了已有的结果.In this paper, we investigate growth problems of solutions of a type of homogeneous and nonhomogeneous higher order linear differential equations with entire coefficients of iterated order. For this type of equations, we obtain precise estimate of iterated order and iterated covergence exponent of the zeros of solutions when some coefficient or free term is mainly dominanting to the properties of the solutions. We also improve the results obtained by some authors.

关 键 词：线性微分方程 整函数 迭代级 迭代收敛指数 小函数 

分 类 号：O174.52[理学—数学] O175.12[理学—基础数学]