| Riccati微分方程特解的向量场分析法 |
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| 引用本文： | 胡博,王明建.Riccati微分方程特解的向量场分析法[J].西安文理学院学报,2010(4):33-35,70. |
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| 作者姓名： | 胡博 王明建 |
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| 作者单位： | [1]河南工业大学理学院,河南郑州450052 [2]郑州师范学院数学系,河南郑州450044 |
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| 基金项目： | 河南省教育厅“十五”教育科学规划重点课题项目（2003—JKCHA—163） |
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| 摘 要： | 对一般的Riccati微分方程,首先给出了在初值条件下解的存在惟一性定理,然后利用向量场的分析方法对其特解进行逼近,最后得到Riccati方程的特解,并讨论了特解的周期性和稳定性.
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| 关 键 词： | Riccati微分方程 向量场 存在惟一性 周期解 稳定性. |
Methods of Vector Field Analysis of Special Solution at Some Riccati Differential Equations |
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| HU Bo,WANG Ming-jian.Methods of Vector Field Analysis of Special Solution at Some Riccati Differential Equations[J].Journal of Xi‘an University of Arts & Science:Natural Science Edition,2010(4):33-35,70. |
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| Authors: | HU Bo WANG Ming-jian |
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| Institution: | 1.College of Sciences,Henan University of Technology,Zhengzhou 450052,China;2.Department of Mathematics,Zhengzhou Normal University,Zhengzhou 450044,China) |
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| Abstract: | This paper gives the theorem of uniqueness of solution existence at initialization conditions for general Riccati differential equations,tries to reach an approximation for special solution by means of vector field,and finally gets a special solution of Riccati differential equations.It also discusses the periodicity and stability of special solution. |
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| Keywords: | Riccati differential equation vector field uniqueness of existence periodic solution stability |
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