Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
7222033 | Nonlinear Analysis: Real World Applications | 2018 | 29 Pages |
Abstract
In this paper, we consider the following quasilinear system: (P)ââi,j=1NDj(aij(u)Diu)+12âi,j=1NDsaij(u)DiuDju=au+|u|2ââ2u+α2â|u|αâ2u|v|βinΩ,ââi,j=1NDj(aij(v)Div)+12âi,j=1NDsaij(v)DivDjv=bv+|v|2ââ2v+β2â|u|α|v|βâ2vinΩ,u=v=0onâΩ,where Di=ââxi,Dsaij(s)=ddsaij(s), a,b>0 are constants, α,β>1 and α+β=2â,2â=2NNâ2 is the Sobolev critical exponent for the embedding of H01(Ω) into Lp(Ω),ΩâRN is an open bounded domain with smooth boundary. By accurate estimates of the concentration compactness and the asymptotic behavior of the approximation solutions to the subcritical problems, we prove that if Nâ¥7, the problem (P) admits infinitely many solutions.
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Authors
Yuxia Guo, Jianjun Nie,