| 一类抽象方程的解集的稳定性与本质连通区 |
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| 引用本文： | 王湘美,蒋 佳. 一类抽象方程的解集的稳定性与本质连通区[J]. 河北科技大学学报, 2011, 32(6): 524-528,535 |
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| 作者姓名： | 王湘美 蒋 佳 |
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| 作者单位： | 1. 贵州大学理学院,贵州贵阳,550025
2. 河北科技大学经济管理学院,河北石家庄,050018 |
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| 摘 要： | 用集值分析的方法,讨论了抽象方程解集的稳定性,得到了通有稳定的结果,并给出了本质连通区存在的充分条件.讨论了抽象方程近似解集的稳定性,得到了通有稳定的结果,同时指出包含精确解的连通分支都是本质的,并且这样的连通分支只有有限个.最后作为应用,对非线性方程组的解集进行了讨论.
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| 关 键 词： | 集值映射 通有稳定性 连通分支 本质连通区 近似解 |
| 收稿时间： | 2011-09-15 |
Stability of solutions to abstract equations andexistence of essential components |
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| WANG Xiang-mei and JIANG Jia. Stability of solutions to abstract equations andexistence of essential components[J]. Journal of Hebei University of Science and Technology, 2011, 32(6): 524-528,535 |
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| Authors: | WANG Xiang-mei and JIANG Jia |
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| Affiliation: | 1. College of Sciences, Guizhou University, Guiyang Ouizhou 550025, China;2. College of Economics and Management, Hebei University of Science and Technology, Shijiazhuang Hebei 050018, China) |
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| Abstract: | By using the method of set-mapping, the stability of the solutions to abstract equations and the existence of essential components is studied. We derived that the solutions have Generic stability. At the same time, a sufficient condition is put for- ward that there is at least one essential component of the solutions when this condition is satisfied. It is derived that the proximal solutions also have generic stability; moreover, the components including exact solutions are essential, and the number of the components which include the exact solutions is finite. Then the stability of the solutions to system of nonlinear equations is analyzed, and a method is proposed to solve problems of system of the nonlinear equations. |
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| Keywords: | set-mapping generic stability component essential component proximal solution |
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