| 局部凸空间中集值映射的极小不动点定理及其应用 |
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| 引用本文： | 徐明跃,曹玉红,王玉文.局部凸空间中集值映射的极小不动点定理及其应用[J].系统科学与数学,2007,27(6):943-952. |
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| 作者姓名： | 徐明跃 曹玉红 王玉文 |
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| 作者单位： | 哈尔滨师范大学数学系,黑龙江,150080 |
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| 基金项目： | 国家自然科学基金;黑龙江省自然科学基金;黑龙江省教育厅科学技术研究项目 |
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| 摘 要： | 利用局部凸空间中Fan-Kakutani不动点定理,得到局部凸空间中集值映射的极小不动点定理,应用此定理,证明了半线性不适定的算子方程的最小范数极值解的存在性.此结果可以应用到不适定常微方程的两点边值问题,不适定偏微方程的边值问题.
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| 关 键 词： | 局部凸空间 集值映射 极小不动点定理 不适定算子方程 |
| 收稿时间： | 2003-2-20 |
| 修稿时间： | 2003年2月20日 |
Minimum Fixed Point Theorem for Set-Valued Mapping in the LocalConvex Space and Its Application |
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| Xu Mingyue,Cao Yuhong,Wang Yuwen.Minimum Fixed Point Theorem for Set-Valued Mapping in the LocalConvex Space and Its Application[J].Journal of Systems Science and Mathematical Sciences,2007,27(6):943-952. |
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| Authors: | Xu Mingyue Cao Yuhong Wang Yuwen |
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| Institution: | Department of Mathematics, Harbin Normal University, Harbin 150080 |
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| Abstract: | In this paper, by Fan-Kakutani fixed point theorem,it is obtained that the minimum fixed point theorem for set-valued mapping in the local convex space. Applyingthis theorem, the existence of the minimal norm extrimal solution to semilinear ill-posed operator equation is proved. The results can be applied to the ill-posed two-points boundary problem for differential equation. |
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| Keywords: | Local convex space set-valued mapping extreme minimum fixed point theorem ill-posed operator equation |
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