Gronwall-Bellman不等式的一个推广
A Refinement of Gronwall-Bellman Inequality

DOI: 10.12677/PM.2016.63037, PP. 238-242

Keywords: Gronwall不等式，矩阵级数，向量
Gronwall Inequality, Matrix Series, Vector

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Abstract:

本文用微分方程组理论和柯西矩阵级数展开作为工具，将Gronwall-Bellman不等式推广成向量形式。
The article modifies Gronwall-Bellman inequality into vector form by the theory of differential equation and Cauchy matrix series expansion.

References

[1]	尤秉礼. 常微分方程补充教程[M]. 北京: 人民教育出版社, 1981.
[2]	王高雄, 周之铭, 朱思铭. 常微分方程[M]. 北京: 高等教育出版社, 2007.
[3]	丁同仁. 常微分方程[M]. 北京: 高等教育出版社, 1978.
[4]	Gronwall, T.H. (1919) Note on the Derivatives with Respect to a Parameter of the Solutions of the Differential Equations. Annals of Mathematics, 20, 292-296.
[5]	Bellman, R. (1943) The Stability of Solutions of Linear Differential Equations. Duke Mathematical Journal, 10, 643- 647. http://dx.doi.org/10.1215/S0012-7094-43-01059-2
[6]	Bihari, I. (1956) Ageneralization of Bellman and Its Application to Uniqueness Problems of Differential Equations. Acta Mathematica Academiae Scientiarum Hungarica, 7, 71-94. http://dx.doi.org/10.1007/BF02022967
[7]	李耀红, 张海燕, 芦伟. Gronwall不等式的新推广[J]. 宿州学院学报(自然科学版), 2008(23): 96-98.
[8]	库连喜. Gronwall-Bellman不等式的一个推广[J]. 华中师范大学学报(自然科学版), 1986(2): 182-184.
[9]	李海春, 刘召梅, 沈亮. Gronwall不等式的推广及应用[J]. 保山学院学报(自然科学版), 2010(2): 55-56.

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