MULTIPLICITY RESULTS FOR A NONLINEAR ELLIPTIC PROBLEM INVOLVING THE FRACTIONAL LAPLACIAN

doi:10.1016/S0252-9602(16)30106-0

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

MULTIPLICITY RESULTS FOR A NONLINEAR ELLIPTIC PROBLEM INVOLVING THE FRACTIONAL LAPLACIAN

许勇强^1,2, 谭忠³, 孙道恒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 XU^1,2, Zhong TAN³, Daoheng SUN¹

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/Abstract

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:

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

中图分类号:

35J99

许勇强, 谭忠, 孙道恒. MULTIPLICITY RESULTS FOR A NONLINEAR ELLIPTIC PROBLEM INVOLVING THE FRACTIONAL LAPLACIAN[J]. 数学物理学报(英文版), 2016, 36(6): 1793-1803.

Yongqiang XU, Zhong TAN, Daoheng SUN. MULTIPLICITY RESULTS FOR A NONLINEAR ELLIPTIC PROBLEM INVOLVING THE FRACTIONAL LAPLACIAN[J]. Acta mathematica scientia,Series B, 2016, 36(6): 1793-1803.

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MULTIPLICITY RESULTS FOR A NONLINEAR ELLIPTIC PROBLEM INVOLVING THE FRACTIONAL LAPLACIAN

MULTIPLICITY RESULTS FOR A NONLINEAR ELLIPTIC PROBLEM INVOLVING THE FRACTIONAL LAPLACIAN

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