高阶亚纯系数非齐次线性微分方程解的零点

邱家亮, 陈宗煊

数学学报 ›› 2014, Vol. 57 ›› Issue (4) : 727-736.

PDF(387 KB)
PDF(387 KB)
数学学报 ›› 2014, Vol. 57 ›› Issue (4) : 727-736. DOI: 10.12386/A2014sxxb0067
论文

高阶亚纯系数非齐次线性微分方程解的零点

    邱家亮, 陈宗煊
作者信息 +

Zeros of Solutions of Higher Order Nonhomogeneous Linear Differential Equations with Meromorphic Coefficients

    Jia Liang QIU, Zong Xuan CHEN
Author information +
文章历史 +

摘要

讨论一类高阶亚纯系数非齐次线性微分方程解的零点问题,当方程的系数A0是亚纯函数且满足δ(∞,A0)=δ(>0)和limr→∞ logTrA0)/log r=∞时,如果f1f2是方程fk + Ak-1fk-1+…+A0f=F的两个线性无关解,得到max{λ(f1),λ(f2)}=∞.还考虑了 sigma(F)=∞或Ad (1≤ dk-1)满足limr→∞ logmrAd)/log r=∞的情况.

Abstract

We investigate the problems of zeros of solutions for some higher order nonhomogeneous linear differential equations. When A0 is a meromorphic function that satisfies δ(∞,A0) = δ(> 0) and limr→∞ logT(rA0)/log r=∞, if f1 and f2 are two linearly independent meromorphic solutions of equation fk + Ak-1fk-1+…+A0f=F,we obtain max{λ(f1),λ(f2)}=∞.And we also investigate the cases that σ(F) = ∞, or some Ad (1≤ dk-1) satisfies limr→∞ logm(rAd)/log r=∞.

关键词

微分方程 / 零点收敛指数 / 增长级

Key words

differential equation / exponent of convergence of zeros / order of growth

引用本文

导出引用
邱家亮, 陈宗煊. 高阶亚纯系数非齐次线性微分方程解的零点. 数学学报, 2014, 57(4): 727-736 https://doi.org/10.12386/A2014sxxb0067
Jia Liang QIU, Zong Xuan CHEN. Zeros of Solutions of Higher Order Nonhomogeneous Linear Differential Equations with Meromorphic Coefficients. Acta Mathematica Sinica, Chinese Series, 2014, 57(4): 727-736 https://doi.org/10.12386/A2014sxxb0067

参考文献

[1] Chen Z. X., On the complex oscillation theory of fk +Af = F, Proc. Edinburgh Mathematical Society, 1993, 36: 447-461.

[2] Chen Z. X., Zero of meromorphic solution of higher order linear differential equatians, Analysis, 1994, 14: 425-438.

[3] Chen Z. X., Gao S. A., On the complex oscillation of non-homogeneous linear differential equatians with polynomial coefficients, Kodai Math. J., 1992, 15: 65-78.

[4] Frank G., Hellerstein S., On the meromorphic solution of non-homogeneous linear differential equatians with polynomial coefficients, Proc. London Math. Soc., 1986, 53(3): 407-428.

[5] Gao S. A., On the complex oscillation of non-homogeneous linear differential equatians with polynomial coefficients, Comment. Math. Univ. Sancti Pauli, 1989, 38(1): 11-20.

[6] Hayman W., Meromorphic Functions, Clarendon Press, Oxford, 1964.

[7] Laine I., A note on the complex oscillation theory of non-homogeneous linear differential equatians, Result in Math., 1990, 18: 282-285.

[8] Yang L., Value Distribution Theory and New Research (in Chinese), Science Press, Beijing, 1982.

基金

国家自然科学基金资助项目(11171119)

PDF(387 KB)

Accesses

Citation

Detail

段落导航
相关文章

/