Existence and stability of normalized solutions to the mixed dispersion nonlinear Schrodinger equations

doi:10.3934/era.2022146

CSpace > 数学所

	Existence and stability of normalized solutions to the mixed dispersion nonlinear Schrodinger equations
	Luo, Haijun 1; Zhang, Zhitao2,3,4
	2022
发表期刊	ELECTRONIC RESEARCH ARCHIVE
卷号	30 期号:8 页码:2871-2898
摘要	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.
关键词	biharmonic nonlinear Schrodinger equations normalized solution orbital stability general nonlinearity
DOI	10.3934/era.2022146
收录类别	SCI
语种	英语
资助项目	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研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000806845600006
出版者	AMER INST MATHEMATICAL SCIENCES-AIMS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/61527
专题	数学所
通讯作者	Zhang, Zhitao
作者单位	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
推荐引用方式 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.