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Triple Positive Solutions of Boundary Value Problems for High-order Fractional Differential Equation at Resonance with Singularities
  
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KeyWord:Triple positive solution; Fractional differential equation; Resonance; Singularity
Author NameAffiliation
Zhiyuan Liu School of Mathematical Sciences, University of Jinan, Jinan, Shandong 250022, China 
Shurong Sun School of Mathematical Sciences, University of Jinan, Jinan, Shandong 250022, China 
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Abstract:
      In this paper, we investigate the existence of triple positive solutions of boundary value problems for high-order fractional differential equation at resonance with singularities by using the fixed point index theory and the Leggett-Williams theorem. The spectral theory and some new height functions are also employed to establish the existence of triple positive solutions. The nonlinearity involved is arbitrary fractional derivative, and permits singularity.