机构地区: 华南师范大学数学科学学院
出 处: 《应用数学学报》 2013年第5期851-861,共11页
摘 要: 在本文中,我们研究了一类高阶齐次线性微分方程f^((k))+A_(k-1)f^((k-1))+…+Aof=0,其中A_j(z)(j=0,1…,k-1)是有限级整函数,且存在A_s(z)(s∈{0,1,…,k-1})是超越的且σ(A_s)<1/2或其泰勒展式为缺项级数.我们给出了方程任一解f≠0的增长估计. In this paper, we consider higher order differential equation f(k)+Ak-1f(k-1)+…A0f=0,where Aj(z)(j=0,1…,k-1) are entire functions of finite order, such that there is some As(z)(s∈{0,1…,k-1})being transcendental with σ(As)〈2^-1or a Fabry power series.We give the estimation of the growth of every solution f≠0 of the equation above.