一类高阶整函数系数微分方程解的增长性  

The growth of solutions of a class of higher order linear differential equations with entire functions coefficents

作　　者：梁建军[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：《宝鸡文理学院学报（自然科学版）》2006年第2期92-95,98,共5页Journal of Baoji University of Arts and Sciences(Natural Science Edition)

摘　　要：目的研究高阶微分方程f(k)+Hk-1f(k-1)+…+H0f=0及f(k)+(Hk-1+gk-1)f(k-1)+…+(H0+g0)f=0的解增长性,其中Hj=hjeajzn+…,hj 0为整函数且σ(hj)<n,aj=djeiφ(dj>0),gj(j=0,…,k-1)。方法应用R.Nevanlinna理论和反证法。结果得到上述2种齐次线性微分方程解的超级的精确估计。结论上述2种齐次线性微分方程将存在大量无穷级解,这类解的超级与方程的系数有密切联系。Aim It was investigated that the growth properties of solutions of a class of higher order linear differential equationsf^（k）＋ Hk-1f^（k-1）＋…＋H0f = 0 and f^（k）＋（Hk-1＋gk-1）f^（k-1）＋…＋（H0 ＋g0）f = 0 , where Hj = hje^ajz^n＋…,hj absolotely uneqvalto 0 and hj is only integral function, σ（hj ） 〈 n, aj =dje^ip （dj〉 0）,gj （j = 0, …,k-1）. Method R. Nevanlinna theory and reduction to absurdity were used. Resuits Some precise estimates for the hyper-order of the solutions of the above-mentioned homogenous linear differential equations were obtained. Conclusion The above-mentioned homogenous linear differential equations have many solutions which are infinite order,and the hyper-order of these solutionshas close liaison with the equation coefficients.

关 键 词：高阶微分方程 整函数 超级 

分 类 号：O174.5[理学—数学]