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| Banach空间中的积分算子不动点定理及其应用 | |
| 引用本文： | 王斌,赵彩红,周丽娜,江卫华.Banach空间中的积分算子不动点定理及其应用[J].数学的实践与认识,2012,42(11):166-171. |
| 作者姓名： | 王斌 赵彩红 周丽娜 江卫华 |
| 作者单位： | 1. 河北化工医药职业技术学院基础部,河北石家庄,050026 2. 石家庄信息工程职业学院,河北石家庄,050035 3. 河北师范大学数学与信息科学学院,河北石家庄,050016 4. 河北科技大学理学院,河北石家庄,050018 |
| 基金项目： | 国家自然科学基金，河北科技大学博士基金，河北省教育厅基金 |
| 摘 要： | 利用不动点指数理论得到了若干个积分算子的不动点定理,这些结论可用于研究许多边值问题.利用这些结论研究了Banach空间中二阶两点边值问题正解的存在性,特别的,在有些情况下去掉了Banach空间中的锥必须是正规的这一条件限制,而这一条件限制在许多文献中是必须的. |
| 关 键 词： | Banach空间 积分算子 Kuratowski非紧性测度 严格集压缩映射 边值问题 |
Multiple Postive Solutions of Nonlinear Multi-Point Boundary Value Problem in Banach Spaces |
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| WANG Bin , ZHAO Cai-hong , ZHOU Li-na , JIANG Wei-hua.Multiple Postive Solutions of Nonlinear Multi-Point Boundary Value Problem in Banach Spaces[J].Mathematics in Practice and Theory,2012,42(11):166-171. | |
| Authors: | WANG Bin ZHAO Cai-hong ZHOU Li-na JIANG Wei-hua |
| Institution: | 1.Department of Basic Courses,Hebei Professional and Technological College of Chemical and Pharmaceutical Engineering,Shijiazhuang 050026,China) (2.Shijiazhuang Information Engineering Vocational College,Shijiazhuang 050035,China) (3.College of Mathematics and Science of Information,Hebei Normal University,Shijiazhuang 050016,China) (4.College of Sciences,Hebei University of Science and Technology,Shijiazhuang 050018,China) |
| Abstract: | Some fixed point theorems of integral operator are given firstly by using fixed point index theory.These results can be used to solve many problems.In this paper,applying these results,we study the existence of positive solutions for two-point boundary value problems in Banach spaces.Particularly,sometimes,we don’t need that the cone in Banach space is normal,which is essential for the technique used in many papers. |
| Keywords: | Banach space integral operator Kuratowski measure of noncompactness strict set contraction boundary value problem |
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