| 计算圆域上p-Henon方程边值问题多个正解的分歧方法 |
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| 引用本文： | 李昭祥,杨忠华.计算圆域上p-Henon方程边值问题多个正解的分歧方法[J].应用数学和力学,2010,31(4):481-490. |
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| 作者姓名： | 李昭祥 杨忠华 |
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| 作者单位： | 1.上海师范大学 计算数学系,上海 200234; |
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| 基金项目： | 国家自然科学基金，上海市学科建设项目，上海市自然科学基金，上海市科委创新资助项目，上海市教委高校优青培养科研专项基金 |
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| 摘 要： | 首先应用分歧方法给出计算p-Henon方程边值问题O(2)对称正解的算法，然后以p-Henon方程中的参数l为分歧参数，在O(2)对称正解解枝上用扩张系统方法求出对称破缺分歧点，进而用解枝转接方法计算出其它具有不同对称性质的正解．
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| 关 键 词： | p-Henon方程 对称破缺分歧 多解 扩张系统 解枝转接 |
| 收稿时间： | 1900-01-01 |
Bifurcation Method for Solving Multiple Positive Solutions to Boundary Value Problem of p-Henon Equation on the Unit Disk |
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| LI Zhao-xiang,YANG Zhong-hua.Bifurcation Method for Solving Multiple Positive Solutions to Boundary Value Problem of p-Henon Equation on the Unit Disk[J].Applied Mathematics and Mechanics,2010,31(4):481-490. |
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| Authors: | LI Zhao-xiang YANG Zhong-hua |
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| Institution: | 1.Department of Mathematics, Shanghai Normal University, Shanghai, 200234, P. R. China;Scientific Computing Key Laboratory of Shanghai University, Shanghai 200234, P. R. China |
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| Abstract: | An algorithm which was applied to solving the O(2) symmetric positive solutions to the boundary value problem of p-Henon equation was proposed. Taking l in p-Henon equation as a bifurcation parameter, the symmetry-breaking bifurcation point on the branch of the O(2) symmetric positive solutions was found via the extended systems. Finally, other symmetric positive solutions were computed by the branch switching method based on the Liapunov-Schmidt reduction. |
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| Keywords: | p-Henon equation symmetry-breaking bifurcation multiple solutions extended system branch switching |
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