复微分方程组的超越解

高凌云

数学学报 ›› 2015, Vol. 58 ›› Issue (1) : 41-48.

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PDF(341 KB)
数学学报 ›› 2015, Vol. 58 ›› Issue (1) : 41-48. DOI: 10.12386/A2015sxxb0004
论文

复微分方程组的超越解

    高凌云
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Transcendental Solutions of Systems of Complex Differential Equations

    Ling Yun GAO
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摘要

利用最大模原理,讨论了复代数微分方程组的超越亚纯解存在性问题,得到了在一定条件下,该方程组的超越解为代数解的一个结果.例子表明这个结果是精确的.

Abstract

Using maximum modulus principle, we investigate the problem of the existence of the transcendental meromorphic solutions of system of complex algebraic differential equations, and obtain a result which the system only the algebraic solution under certain conditions. Examples show that our results are sharp.

关键词

代数解 / 超越亚纯函数 / 微分方程 / 最大模原理

Key words

algebraic solution / transcendental meromorphic function / differential equations / maximum modulus principle

引用本文

导出引用
高凌云. 复微分方程组的超越解. 数学学报, 2015, 58(1): 41-48 https://doi.org/10.12386/A2015sxxb0004
Ling Yun GAO. Transcendental Solutions of Systems of Complex Differential Equations. Acta Mathematica Sinica, Chinese Series, 2015, 58(1): 41-48 https://doi.org/10.12386/A2015sxxb0004

参考文献

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[7] He Y. Z., Xiao X. Z., Algebroid Functions and Ordinary Differential Equations (in Chinese), Science Press, Beijing, 1988.

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[9] Song S. G., Meromorphic solutions of differential equations in the complex domain, Acta Mathematica Sinica, Chinese Series, 1991, 34: 779-784.

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基金

国家自然科学基金资助项目(10471065);广东省自然科学基金资助项目(04010474)

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