KMS Of Academy of mathematics and systems sciences, CAS
Infinitely many solutions for quasilinear systems with critical exponent | |
Guo, Yuxia1; Nie, Jianjun2 | |
2018-10-01 | |
Source Publication | NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS |
ISSN | 1468-1218 |
Volume | 43Pages:378-406 |
Abstract | In 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. |
Keyword | Quasilinear system Infinitely many solutions Critical exponent |
DOI | 10.1016/j.nonrwa.2018.03.008 |
Language | 英语 |
Funding Project | NSFC[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 Area | Mathematics |
WOS Subject | Mathematics, Applied |
WOS ID | WOS:000433655300019 |
Publisher | PERGAMON-ELSEVIER SCIENCE LTD |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/30554 |
Collection | 中国科学院数学与系统科学研究院 |
Affiliation | 1.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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