一类具有缺项级数系数的高阶微分方程解的增长性  

GROWTH OF SOLUTIONS OF A CLASS OF HIGHER-ORDER DIFFERENTIAL EQUATIONS WITH COEFFICIENTS HAVING FABRY GAP

作　　者：陈美茹[1] 陈宗煊[1] 

机构地区：[1]华南师范大学数学科学学院,广东广州510631

出　　处：《华南师范大学学报（自然科学版）》2011年第4期26-30,共5页Journal of South China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(10871076)

摘　　要：研究了高阶非齐次微分方程f(k)+Ak-1f(k-1)+…+A1f′+A0f=F,其中A0,A1,…,F是整函数.当存在某个系数Ad为缺项级数并对方程的解的性质起主要支配作用时,得到上述微分方程和对应的齐次微分方程在一定条件下超越解超级的精确估计.The growth of solutions for a class of higher-order nonhomogeneous linear differential equation f（k）＋Ak-1 f（k-1）＋…＋A1 f ′＋A0 f=F and its corresponding homogeneous linear differential equation,is investigated,where A0,A1,…,F are entire functions and the dominant coefficient Ad has a fabry gap.General estimates of the growth and zeros of entire transcendental solutions of the above equations are obtained.

关 键 词：NEVANLINNA理论 微分方程 缺项级数 超级 

分 类 号：O175.29[理学—数学]