具有缺项级数系数的高阶齐次线性微分方程解的性质  

The Properties of Solutions to Higher-order Homogeneous Linear Differential Equations with Coefficient of 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,广州510631

出　　处：《数学物理学报（A辑）》2011年第6期1697-1707,共11页Acta Mathematica Scientia

基　　金：国家自然科学基金(10871076;11171119)资助

摘　　要：该文研究了高阶齐次微分方程f^((k))+A_(k-2)f^((k-2))+…+A_1f′+A_0f=0.其中A_0,…,A_((k-2))为具有有限个极点的亚纯函数,当存在某个系数A_s(s∈{2,….k-2})为缺项级数并对方程的解的性质起着主要支配作用时,得到上述微分方程的线性无关超越解的最少个数和零点收敛指数为有穷的解的最多个数.In the paper, the authors investigate the exponent of convergence of the zero- sequence of meromorphic solutions to homogeneous linear differential equation f（k）＋Ak-2f（k-2）＋ …＋ A1f′ ＋ Aof = 0 when its coefficients are meromorphic functions possessing only a finite number of poles and dominant coefficient As（s ∈ {2,…, k - 2）） is fabry gap. The minimum number of linear independent transcendental solutions and the maximum number of linear in- dependent transcendental solutions with finite exponents of convergence of the zero-sequence are obtained.

关 键 词：微分方程 缺项级数 线性无关 零点收敛指数. 

分 类 号：O175.29[理学—数学]