Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8053508 | Applied Mathematics Letters | 2018 | 7 Pages |
Abstract
We consider the Brézis-Nirenbergproblem: {âÎu=|u|2ââ2u+λuinΩ,u=0onâΩ,where Ω is a smooth bounded domain in RN,Nâ¥3,2â=2NNâ2 is the critical Sobolev exponent and λ>0. Our main result asserts that if Nâ¥4 then there exists a pair of sign-changing solutions of the problem for every λâ(0,λ1(Ω)), λ1(Ω) being the first eigenvalue of âÎ in Ω with Dirichlet boundary conditions, while if N=3 then a pair of sign-changing solutions exists for λ slightly smaller than λ1(Ω). Our approach uses variational methods together with flow invariance arguments.
Related Topics
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Authors
Tieshan He, Chaolong Zhang, Dongqing Wu, Kaihao Liang,