JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2019, Vol. 54 ›› Issue (10): 57-66.doi: 10.6040/j.issn.1671-9352.0.2018.302

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Existence of positive solutions for fractional nonhomogeneous boundary value problem with p-Laplacian

SONG Jun-qiu, JIA Mei*, LIU Xi-ping, LI Lin   

  1. College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China
  • Published:2019-10-12

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Abstract: We study the existence of positive solutions for integral boundary value problem of fractional p-Laplacian equation with disturbance parameters. According to the properties of integral kernel and using the cone expansion and cone compression fixed point theorem and the super-linear and sub-linear conditions, the sufficient conditions of existence and nonexistence of positive solutions for the boundary value problem are obtained. The conclusions show the impact of parameters on the existence of positive solutions. Finally, we give some examples to illustrate our main results.

Key words: fractional differential equation, p-Laplacian operator, disturbance parameter, fixed point theorem, positive solution

CLC Number: 

  • O175.8
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