数学物理学报(英文版) ›› 2016, Vol. 36 ›› Issue (6): 1793-1803.doi: 10.1016/S0252-9602(16)30106-0

• 论文 • 上一篇    下一篇

MULTIPLICITY RESULTS FOR A NONLINEAR ELLIPTIC PROBLEM INVOLVING THE FRACTIONAL LAPLACIAN

许勇强1,2, 谭忠3, 孙道恒1   

  1. 1. Department of Mechanical and Electrical Engineering, Xiamen University, Xiamen 361005, China;
    2. School of Mathematics and Statistics, Minnan Normal University, Zhangzhou 363000, China;
    3. School of Mathematical Sciences, Xiamen University, Xiamen 361005, China
  • 收稿日期:2015-04-04 修回日期:2016-05-12 出版日期:2016-12-25 发布日期:2016-12-25
  • 作者简介:Yongqiang XU,E-mail:yqx458@126.com;Zhong TAN,E-mail:ztan85@163.com;Daoheng SUN,E-mail:sundh@xmu.edu.cn
  • 基金资助:

    This research was supported by China Postdoctoral Science Foundation Funded Project (2016M592088) and National Natural Science Foundation of China-NSAF (11271305).

MULTIPLICITY RESULTS FOR A NONLINEAR ELLIPTIC PROBLEM INVOLVING THE FRACTIONAL LAPLACIAN

Yongqiang XU1,2, Zhong TAN3, Daoheng SUN1   

  1. 1. Department of Mechanical and Electrical Engineering, Xiamen University, Xiamen 361005, China;
    2. School of Mathematics and Statistics, Minnan Normal University, Zhangzhou 363000, China;
    3. School of Mathematical Sciences, Xiamen University, Xiamen 361005, China
  • Received:2015-04-04 Revised:2016-05-12 Online:2016-12-25 Published:2016-12-25
  • Supported by:

    This research was supported by China Postdoctoral Science Foundation Funded Project (2016M592088) and National Natural Science Foundation of China-NSAF (11271305).

摘要:

In this paper, we consider a class of superlinear elliptic problems involving fractional Laplacian (-Δ)s/2u=λf(u) in a bounded smooth domain with zero Dirichlet boundary condition. We use the method on harmonic extension to study the dependence of the number of sign-changing solutions on the parameter λ.

关键词: fractional Laplacian, existence, asymptotic, Sobolev trace inequality

Abstract:

In this paper, we consider a class of superlinear elliptic problems involving fractional Laplacian (-Δ)s/2u=λf(u) in a bounded smooth domain with zero Dirichlet boundary condition. We use the method on harmonic extension to study the dependence of the number of sign-changing solutions on the parameter λ.

Key words: fractional Laplacian, existence, asymptotic, Sobolev trace inequality

中图分类号: 

  • 35J99