Acta mathematica scientia,Series B ›› 2016, Vol. 36 ›› Issue (6): 1819-1831.doi: 10.1016/S0252-9602(16)30108-4

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THREE SOLUTIONS FOR A FRACTIONAL ELLIPTIC PROBLEMS WITH CRITICAL AND SUPERCRITICAL GROWTH

Jinguo ZHANG1, Xiaochun LIU2   

  1. 1. School of Mathematics, Jiangxi Normal University, Nanchang 330022, China;
    2. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
  • Received:2016-02-09 Revised:2016-04-28 Online:2016-12-25 Published:2016-12-25
  • Supported by:

    Supported by NSFC (11371282, 11201196) and Natural Science Foundation of Jiangxi (20142BAB211002).

Abstract:

In this paper, we deal with the existence and multiplicity of solutions to the fractional elliptic problems involving critical and supercritical Sobolev exponent via variational arguments. By means of the truncation combining with the Moser iteration, we prove that our problem has at least three solutions.

Key words: fractional elliptic equation, variational methods, three solutions, Moser iteration

CLC Number: 

  • 35J60
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