单位圆内某类高阶微分方程解的增长性  

The Growth of Solutions for Some Kind of Higher Order Differential Equations in the Unit Disc

作　　者：龚攀[1] 吴红星[1] GONG Pan;WU Hongxing(School of Mathematics and Computational Science,Shangrao Normal University,334001,Shangrao,Jiangxi,PRC)

机构地区：[1]上饶师范学院数学与计算科学学院,江西上饶334001

出　　处：《江西科学》2024年第6期1141-1147,共7页Jiangxi Science

基　　金：国家自然科学基金项目(12161074,12163003);江西省教育厅科学技术研究项目(GJJ2401702)。

摘　　要：研究高阶齐次线性微分方程f^(n)+A_(n-1)(z)f^(n-1)+…+A_(1)(z)f'+A_(0)(z)f=0解的增长性,其中系数是单位圆Δ内的解析函数。当A_(0)(z)和A_(s)(z)的[p,q]下级,[p,q]下型或者[p,q]下新型控制其他的系数,得到了解的[p,q]级的估计。The paper studies the growth of solutions to the higher order homogeneous linear differential equation,f^(n)+A_(n-1)(z)f^(n-1)+…+A_(1)(z)f'+A_(0)(z)f=0 where the coefficients are analytic functions in the unit discΔ.When A_(0)(z)andA_(s)(z)dominate the other coefficients,we obtain some estimates of[p,q]-orderof solutions of the equation by using the lower[p,q]-order,the lower[p,q]-type or the lower new[p,q]-type of A0(z)to As(z).

关 键 词：单位圆 解析系数 [p q]新型 

分 类 号：O174.52[理学—数学]