JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2016, Vol. 51 ›› Issue (6): 78-84.doi: 10.6040/j.issn.1671-9352.0.2015.632

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Positive solutions for some singular fractional differential equation integral boundary value problems with p-Laplacian and a parameter

ZHONG Qiu-yan1, ZHANG Xing-qiu2,3   

  1. 1. Department of Information Technology, Jining Medical College, Jining 272067, Shandong, China;
    2. School of Medical Information Engineering, Jining Medical College, Rizhao 276826, Shandong, China;
    3. School of Mathematics, Liaocheng University, Liaocheng 252059, Shandong, China
  • Received:2015-12-29 Online:2016-06-20 Published:2016-06-15

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Abstract: A special cone is constructed by means of the properties of Green function. By introducing height functions of the nonlinear term on some bounded sets and considering integrations of these height functions, several existence and multiplicity of local positive solutions theorems for some nonlinear fractional differential equation integral boundary value problems with p-Laplacian and a parameter are obtained. The nonlinear term f permits singularities with respect to both the time and space variables.

Key words: fractional differential equation, singularity, p-Laplacian, height functions

CLC Number: 

  • O175.8
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