数学物理学报(英文版) ›› 2016, Vol. 36 ›› Issue (6): 1819-1831.doi: 10.1016/S0252-9602(16)30108-4

• 论文 • 上一篇    下一篇

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

张金国1, 刘晓春2   

  1. 1. School of Mathematics, Jiangxi Normal University, Nanchang 330022, China;
    2. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
  • 收稿日期:2016-02-09 修回日期:2016-04-28 出版日期:2016-12-25 发布日期:2016-12-25
  • 作者简介:Jinguo ZHANG,E-mail:jgzhang@jxnu.edu.cn;Xiaochun LIU,E-mail:xcliu@whu.edu.cn
  • 基金资助:

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

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).

摘要:

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.

关键词: fractional elliptic equation, variational methods, three solutions, Moser iteration

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

中图分类号: 

  • 35J60