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具有缺项级数系数的高阶齐次线性微分方程解的性质
  • 期刊名称：数学物理学报, 31(6)(2011), 1697—1707.
  • 时间：0
  • 分类：O175.29[理学—数学;理学—基础数学]
  • 作者机构：[1]华南师范大学数学科学学院,广州510631
  • 相关基金：基金项目：国家自然科学基金（10871076,11171119）资助
  • 相关项目：复域差分, 差分方程与微分方程的解析性质
关键词： 微分方程, 缺项级数, 线性无关, 零点收敛指数., Differential equation, Fabry gap, Linearly independent, Exponent of convergenceof zero-sequence.
中文摘要：

该文研究了高阶齐次微分方程f（k）＋Ak-2f（k-2）＋…＋A1F′＋A0f=0,其中A0，…，Ak-2为具有有限个极点的亚纯函数，当存在某个系数As（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．

英文摘要：

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.

同期刊论文项目
复域差分, 差分方程与微分方程的解析性质
期刊论文 62
复域差分, 差分方程和微分方程的研究
期刊论文 126 著作 1
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