| 奇点处分岔解支的数目问题* |
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| 引用本文： | 周鹍.奇点处分岔解支的数目问题*[J].应用数学和力学,1997,18(10):905-909. |
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| 作者姓名： | 周鹍 |
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| 作者单位： | 北京大学力学与工程科学系, 北京 100871 |
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| 基金项目： | 国家自然科学基金，非线性科学攀登计划资助项目 |
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| 摘 要： | 本文在孤立奇点的假设下证明了带参数非线性方程组解的孤立性,同时指出在分岔点处必有而且仅有有限条解支分岔出来．这一结论是分岔问题数值方法的一个理论基础．
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| 关 键 词： | 同伦 延续算法 分岔 孤立奇点 |
| 收稿时间： | 1995-07-19 |
On the Problem of the Number of Bifurcation Solutions at Singular Point |
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| Zhou Kun.On the Problem of the Number of Bifurcation Solutions at Singular Point[J].Applied Mathematics and Mechanics,1997,18(10):905-909. |
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| Authors: | Zhou Kun |
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| Institution: | Department of Mechanics and Engineering Science, Peking University, Bejing 100871, P. R. China |
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| Abstract: | In this paper, it is proved that the'solutions of a nonlinear equation are isolated under the condition that the singular points are isolated. It shows that there must have and only have finite solutions branching from bifurcation point.This is important for the numerical analysis of bifurcation problems. |
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| Keywords: | homotopy continuation method bifurcation isolated singularity |
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