| Multiple Positive Solutions for Multi-Point Boundary Value Problem of Fractional Differential Equation |
| Received:April 25, 2016 Revised:November 02, 2016 |
| Key Words:
fractional differential equation multi-point boundary value problem positive solution Green function fixed point theorem
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11171220) and the Hujiang Foundation of China (Grant No.B14005). |
| Author Name | Affiliation | | Xiping LIU | College of Science, University of Shanghai for Science and Technology, Shanghai 200093, P. R. China | | Mei JIA | College of Science, University of Shanghai for Science and Technology, Shanghai 200093, P. R. China | | Ming NIU | Department of Mechanics and Electronics, Shijiazhuang Vocational Technology Institute, Hebei 050081, P. R. China | | Xiufen XIANG | 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. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2017.02.011 |
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