| 分数阶微分方程多点边值问题的正解 |
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| 引用本文： | 刘锡平,贾梅,牛铭,相秀芬.分数阶微分方程多点边值问题的正解[J].数学研究及应用,2017,37(2):223-232. |
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| 作者姓名： | 刘锡平 贾梅 牛铭 相秀芬 |
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| 作者单位： | 上海理工大学理学院, 上海 200093,上海理工大学理学院, 上海 200093,石家庄职业技术学院机电工程系, 河北 石家庄 050081,承德石油高等专科学校社科与数理部, 河北 承德 067000 |
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| 基金项目： | 国家自然科学基金(Grant No.11171220),沪江基金(Grant No.B14005). |
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| 摘 要： | 本文研究了在边界条件中含有多个分数导数项的分数阶微分方程多点边值问题多个正解的存在性.运用Green函数的性质以及有白-葛推导出的一般形式的Leggett-Williams不动点定理,建立了边值问题至少有三个正解存在的充分条件.最后,给出了一个例子,用于说明所得主要结论具有广泛的适用性.
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| 关 键 词： | 分数阶微分方程 多点边值问题 正解 Green函数 不动点定理 |
| 收稿时间： | 2016/4/25 0:00:00 |
| 修稿时间： | 2016/11/2 0:00:00 |
Multiple Positive Solutions for Multi-Point Boundary Value Problem of Fractional Differential Equation |
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| Xiping LIU,Mei JIA,Ming NIU and Xiufen XIANG.Multiple Positive Solutions for Multi-Point Boundary Value Problem of Fractional Differential Equation[J].Journal of Mathematical Research with Applications,2017,37(2):223-232. |
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| Authors: | Xiping LIU Mei JIA Ming NIU and Xiufen XIANG |
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| Institution: | College of Science, University of Shanghai for Science and Technology, Shanghai 200093, P. R. China,College of Science, University of Shanghai for Science and Technology, Shanghai 200093, P. R. China,Department of Mechanics and Electronics, Shijiazhuang Vocational Technology Institute, Hebei 050081, P. R. China and Department of Mathematics and Physics, Chengde Petroleum College, Hebei 067000, P. R. China |
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| Abstract: | In this paper, we study the multiplicity of positive solutions for multi-point boundary value problem of Riemann-Liouville fractional differential equation with multi-terms fractional derivative in the boundary conditions. By using the properties of the Green function and a generalization of the Leggett-Williams fixed point theorem due to the work of Bai and Ge, the sufficient conditions to guarantee the existence of at least three positive solutions are established. In the end of this paper, we have also given out the example to illustrate the wide range of potential application of our main results. |
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| Keywords: | fractional differential equation multi-point boundary value problem positive solution Green function fixed point theorem |
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