Acta mathematica scientia, Series B >
MULTIPLICITY RESULTS FOR A NONLINEAR ELLIPTIC PROBLEM INVOLVING THE FRACTIONAL LAPLACIAN
Received date: 2015-04-04
Revised date: 2016-05-12
Online 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).
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
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 . DOI: 10.1016/S0252-9602(16)30106-0
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