Multiple Positive Solutions for Multi-Point Boundary Value Problem of Fractional Differential Equation
Received:April 25, 2016  Revised:November 02, 2016
Key Word: fractional differential equation   multi-point boundary value problem   positive solution   Green function   fixed point theorem  
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant No.11171220) and the Hujiang Foundation of China (Grant No.B14005).
Author NameAffiliation
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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