Infinitely many solutions for quasilinear systems with critical exponent
Guo, Yuxia1; Nie, Jianjun2
AbstractIn this paper, we consider the following quasilinear system: { - Sigma(N)(i,j=1) D-j(a(ij)(u)D(i)u) + 1/2 Sigma(N)(i,j=1) D(s)a(ij)(u)D(i)uD(j)u = au + vertical bar u vertical bar(2*-2)u + alpha/2* vertical bar u vertical bar(alpha-2)u vertical bar v vertical bar(beta) in Omega, - Sigma(N)(i,j=1) D-j(a(ij)(v)D(i)v) + 1/2 Sigma(N)(i,j=1) D(s)a(ij)(v)D(i)vD(j)v = bv + vertical bar v vertical bar(2*-2)v + beta/2* vertical bar u vertical bar(alpha)vertical bar v vertical bar(beta-2) in Omega, u=v=0 on partial derivative Omega, where D-i = partial derivative/partial derivative x(i), D(s)a(ij)(s) = d/ds a(ij)(s), a,b > 0 are constants, alpha,beta > 1 and alpha + beta = 2*, 2* = 2N/N-2 is the Sobolev critical exponent for the embedding of H-0(1) (Omega) into L-P(Omega), Omega subset of R-N 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 N >= 7, the problem (P) admits infinitely many solutions. (C) 2018 Elsevier Ltd. All rights reserved.
KeywordQuasilinear system Infinitely many solutions Critical exponent
Funding ProjectNSFC[11331010] ; NSFC[11771235] ; China Postdoctoral Science Foundation[2017M620934] ; Specialized Fund for Science and Technology Platform and Talent Team Project of Guizhou Province[QianKeHePingTaiRenCai [2016]5609]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000433655300019
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Document Type期刊论文
Corresponding AuthorNie, Jianjun
Affiliation1.Tsinghua Univ, Dept Math, Beijing 100084, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Math, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Guo, Yuxia,Nie, Jianjun. Infinitely many solutions for quasilinear systems with critical exponent[J]. NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS,2018,43:378-406.
APA Guo, Yuxia,&Nie, Jianjun.(2018).Infinitely many solutions for quasilinear systems with critical exponent.NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS,43,378-406.
MLA Guo, Yuxia,et al."Infinitely many solutions for quasilinear systems with critical exponent".NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS 43(2018):378-406.
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