Existence and stability of normalized solutions to the mixed dispersion nonlinear Schrodinger equations | |
Luo, Haijun1; Zhang, Zhitao2,3,4 | |
2022 | |
Source Publication | ELECTRONIC RESEARCH ARCHIVE |
Volume | 30Issue:8Pages:2871-2898 |
Abstract | We 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. |
Keyword | biharmonic nonlinear Schrodinger equations normalized solution orbital stability general nonlinearity |
DOI | 10.3934/era.2022146 |
Indexed By | SCI |
Language | 英语 |
Funding Project | National 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 Area | Mathematics |
WOS Subject | Mathematics |
WOS ID | WOS:000806845600006 |
Publisher | AMER INST MATHEMATICAL SCIENCES-AIMS |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/61527 |
Collection | 数学所 |
Corresponding Author | Zhang, Zhitao |
Affiliation | 1.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. |
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