Construction of solutions for the polyharmonic equation via local Pohozaev identities

doi:10.1007/s00526-019-1569-1

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	Construction of solutions for the polyharmonic equation via local Pohozaev identities
	Guo, Yuxia 1; Liu, Ting 1; Nie, Jianjun 2
	2019-08-01
Source Publication	CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
ISSN	0944-2669
Volume	58 Issue:4 Pages:33
Abstract	We consider the following problem involving critical exponent and polyharmonic operator: (-Delta)(m)u + V(vertical bar y'vertical bar, y '')u = u(m-1), u > 0, u is an element of D-m,D-2 (R-N), where m = 2N/N-2m, N >= 4m + 1, m is an element of N+, (y', y '') is an element of R-2 x RN-2 and V(vertical bar y'vertical bar , vertical bar y ''vertical bar) is a bounded non-negative function in R+ x RN-2. By using a finite reduction argument and local Pohozaev type identities, we will show that if N >= 4m + 1 and r(2m)V(r, y '') has a stable critical point (r(0), y(0)''), then the above problem has infinitely many solutions, whose energy can be arbitrarily large.
DOI	10.1007/s00526-019-1569-1
Language	英语
Funding Project	NSFC[11771235] ; NSFC[11801545]
WOS Research Area	Mathematics
WOS Subject	Mathematics, Applied ; Mathematics
WOS ID	WOS:000474383500003
Publisher	SPRINGER HEIDELBERG
Citation statistics
Document Type	期刊论文
Identifier	http://ir.amss.ac.cn/handle/2S8OKBNM/35185
Collection	中国科学院数学与系统科学研究院
Corresponding Author	Guo, Yuxia
Affiliation	1.Tsinghua Univ, Dept Math Sci, Beijing, Peoples R China 2.Chinese Acad Sci, Inst Math Acad Math & Syst Sci, Beijing 100190, Peoples R China
Recommended Citation GB/T 7714	Guo, Yuxia,Liu, Ting,Nie, Jianjun. Construction of solutions for the polyharmonic equation via local Pohozaev identities[J]. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS,2019,58(4):33.
APA	Guo, Yuxia,Liu, Ting,&Nie, Jianjun.(2019).Construction of solutions for the polyharmonic equation via local Pohozaev identities.CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS,58(4),33.
MLA	Guo, Yuxia,et al."Construction of solutions for the polyharmonic equation via local Pohozaev identities".CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS 58.4(2019):33.

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