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一类二阶自治微分方程的代数曲线解的存在性问题

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一类二阶自治微分方程的代数曲线解的存在性问题 杜小飞, 胡彦霞华北电力大学数理学院, 北京 102206 The Existence of Algebraic Curve Solutions for a Class of Second Order Autonomous Differential Equations DU Xiaofei, HU YanxiaSchool of Mathematics and Physics, North China Electric Power University, Beijing 102206, China
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摘要本文考虑了一类二阶自治系统的代数曲线解的存在性问题.利用整除定理给出了这类系统不具有代数曲线解的几个条件;证明了如果这类系统是Liouville可积的,则一定有代数曲线解.
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收稿日期: 2018-07-17

引用本文:
杜小飞, 胡彦霞. 一类二阶自治微分方程的代数曲线解的存在性问题[J]. 应用数学学报, 2019, 42(5): 701-711. DU Xiaofei, HU Yanxia. The Existence of Algebraic Curve Solutions for a Class of Second Order Autonomous Differential Equations. Acta Mathematicae Applicatae Sinica, 2019, 42(5): 701-711.
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http://123.57.41.99/jweb_yysxxb/CN/ http://123.57.41.99/jweb_yysxxb/CN/Y2019/V42/I5/701


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