| 计算单位球上Henon方程正解的分歧方法 |
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| 引用本文： | 李昭祥,杨忠华,朱海龙.计算单位球上Henon方程正解的分歧方法[J].山西大学学报(自然科学版),2010,33(4). |
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| 作者姓名： | 李昭祥 杨忠华 朱海龙 |
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| 作者单位： | 上海师范大学计算数学系;上海师范大学科学计算上海高校重点实验室;安徽财经大学统计与应用数学学院; |
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| 基金项目： | 国家自然科学基金，上海重点学科建设项目，上海市自然科学基金，上海师范大学科研项目，上海市科委创新项目，上海市教委高校优青培养科研专项基金，安徽省高等学校优秀青年人才基金 |
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| 摘 要： | 首先应用分歧方法计算单位球上Henon方程边值问题O(3)对称正解,然后以Henon方程中的参数l为分歧参数,在O(3)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具有其它对称性质的正解.
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| 关 键 词： | Henon方程 对称破缺分歧 扩张系统 解枝转接 |
Computing the Multiple Solutions to Boundary Value Problem of Henon Equation on the Unit Ball of Space |
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| LI Zhao-xiang,YANG Zhong-hua,ZHU Hai-long.Computing the Multiple Solutions to Boundary Value Problem of Henon Equation on the Unit Ball of Space[J].Journal of Shanxi University (Natural Science Edition),2010,33(4). |
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| Authors: | LI Zhao-xiang YANG Zhong-hua ZHU Hai-long |
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| Institution: | LI Zhao-xiang1,YANG Zhong-hua2,ZHU Hai-long3(1.Computing Mathematics Department,Shanghai Normal University,Shanghai 200234,China,2.Scientific Computing Key Laboratory of Shanghai Universities,3.School of Statistics and Applied Mathematics,Anhui University of Finance &Economics,Bengbu 233030,China) |
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| Abstract: | We apply the bifurcation method to solving the O(3) symmetric positive solutions to the boundary value problem of Henon equation.Taking l in Henon equation as a bifurcation parameter,the symmetry-breaking bifurcation point on the branch of the O(3) symmetric positive solutions is fund via the extended systems.Moreover,the other symmetric positive solutions are computed by the branch switching method based on the liapunov-Schmidt reduction. |
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| Keywords: | Henon equation symmetry-breaking bifurcation extended system branch switching |
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