Infinitely many solutions for quasilinear systems with critical exponent

doi:10.1016/j.nonrwa.2018.03.008

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	Infinitely many solutions for quasilinear systems with critical exponent
	Guo, Yuxia 1; Nie, Jianjun 2
	2018-10-01
发表期刊	NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
ISSN	1468-1218
卷号	43 页码:378-406
摘要	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.
关键词	Quasilinear system Infinitely many solutions Critical exponent
DOI	10.1016/j.nonrwa.2018.03.008
语种	英语
资助项目	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研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000433655300019
出版者	PERGAMON-ELSEVIER SCIENCE LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/30554
专题	中国科学院数学与系统科学研究院
通讯作者	Nie, Jianjun
作者单位	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
推荐引用方式 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.