CSpace  > 数学所
Existence and stability of normalized solutions to the mixed dispersion nonlinear Schrodinger equations
Luo, Haijun1; Zhang, Zhitao2,3,4
2022
Source PublicationELECTRONIC RESEARCH ARCHIVE
Volume30Issue:8Pages:2871-2898
AbstractWe study the existence and orbital stability of normalized solutions of the biharmonic equation with the mixed dispersion and a general nonlinear term gamma Delta(2)u - beta Delta u + lambda u = f(u), x is an element of R-N with a priori prescribed L-2-norm constraint S-a := {u is an element of H-2(R-N) : integral R-N |u|(2)dx = ao, where a > 0, gamma > 0, beta. R and the nonlinear term f satisfies the suitable L-2-subcritical assumptions. When beta >= 0, we prove that there exists a threshold value a(0) >= 0 such that the equation above has a ground state solution which is orbitally stable if a > a0 and has no ground state solution if a < a(0). However, for beta < 0, this case is more involved. Under an additional assumption on f, we get the similar results on the existence and orbital stability of ground state. Finally, we consider a specific nonlinearity f (u) = |u|(p-2)u + mu|u|(q-2)u, 2 < q < p < 2 + 8/N, mu < 0 under the case beta < 0, which does not satisfy the additional assumption. And we use the example to show that the energy in the case beta < 0 exhibits a more complicated nature than that of the case beta = 0.
Keywordbiharmonic nonlinear Schrodinger equations normalized solution orbital stability general nonlinearity
DOI10.3934/era.2022146
Indexed BySCI
Language英语
Funding ProjectNational Natural Science Foundation of China[11901182] ; National Natural Science Foundation of China[12031015] ; National Natural Science Foundation of China[11771428] ; National Natural Science Foundation of China[12026217] ; Natural Science Foundation of Hunan Province[2021JJ40033] ; Fundamental Research Funds for the Central Universities[531118010205]
WOS Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000806845600006
PublisherAMER INST MATHEMATICAL SCIENCES-AIMS
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/61527
Collection数学所
Corresponding AuthorZhang, Zhitao
Affiliation1.Hunan Univ, Sch Math, Hunan Prov Key Lab Intelligent Informat Proc & Ap, Changsha 410082, Hunan, Peoples R China
2.Jiangsu Univ, Sch Math Sci, Zhenjiang 212013, Jiangsu, Peoples R China
3.Chinese Acad Sci, Acad Math & Syst Sci, HLM, Beijing 100190, Peoples R China
4.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
Recommended Citation
GB/T 7714
Luo, Haijun,Zhang, Zhitao. Existence and stability of normalized solutions to the mixed dispersion nonlinear Schrodinger equations[J]. ELECTRONIC RESEARCH ARCHIVE,2022,30(8):2871-2898.
APA Luo, Haijun,&Zhang, Zhitao.(2022).Existence and stability of normalized solutions to the mixed dispersion nonlinear Schrodinger equations.ELECTRONIC RESEARCH ARCHIVE,30(8),2871-2898.
MLA Luo, Haijun,et al."Existence and stability of normalized solutions to the mixed dispersion nonlinear Schrodinger equations".ELECTRONIC RESEARCH ARCHIVE 30.8(2022):2871-2898.
Files in This Item:
There are no files associated with this item.
Related Services
Recommend this item
Bookmark
Usage statistics
Export to Endnote
Google Scholar
Similar articles in Google Scholar
[Luo, Haijun]'s Articles
[Zhang, Zhitao]'s Articles
Baidu academic
Similar articles in Baidu academic
[Luo, Haijun]'s Articles
[Zhang, Zhitao]'s Articles
Bing Scholar
Similar articles in Bing Scholar
[Luo, Haijun]'s Articles
[Zhang, Zhitao]'s Articles
Terms of Use
No data!
Social Bookmark/Share
All comments (0)
No comment.
 

Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.