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Construction of solutions for the polyharmonic equation via local Pohozaev identities
Guo, Yuxia1; Liu, Ting1; Nie, Jianjun2
2019-08-01
Source PublicationCALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
ISSN0944-2669
Volume58Issue:4Pages:33
AbstractWe 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.
DOI10.1007/s00526-019-1569-1
Language英语
Funding ProjectNSFC[11771235] ; NSFC[11801545]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000474383500003
PublisherSPRINGER HEIDELBERG
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/35185
Collection中国科学院数学与系统科学研究院
Affiliation1.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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