Normalized solutions to the fractional Schrodinger equations with combined nonlinearities

doi:10.1007/s00526-020-01814-5

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	Normalized solutions to the fractional Schrodinger equations with combined nonlinearities
	Luo, Haijun 3; Zhang, Zhitao 1,2
刊名	CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
	2020-08-13
卷号	59 期号:4 页码:35
ISSN号	0944-2669
DOI	10.1007/s00526-020-01814-5
英文摘要	We study the normalized solutions of the fractional nonlinear Schrodinger equations with combined nonlinearities (-Delta)(s)u = lambda u + mu vertical bar u vertical bar(q-2)u + vertical bar u vertical bar(p-2)u in R-N, and we look for solutions which satisfy prescribed mass integral(RN) vertical bar u vertical bar(2) = a(2), where N >= 2, s is an element of (0, 1), mu is an element of R and 2 < q < p < 2*(s) = 2N/(N - 2s). Under different assumptions on q < p, a > 0 and mu is an element of R, we prove some existence and nonexistence results about the normalized solutions. More specifically, in the purely L-2-subcritical case, we overcome the lack of compactness by virtue of the monotonicity of the least energy value and obtain the existence of ground state solution for mu > 0. While for the defocusing situation mu < 0, we prove the nonexistence result by constructing an auxiliary function. We emphasis that the nonexistence result is new even for Laplacian operator. In the purely L-2-supercritical case, we introduce a fiber energy functional to obtain the boundedness of the Palais-Smale sequence and get a mountain-pass type solution. In the combined-type cases, we construct different linking structures to obtain the saddle type solutions. Finally, we remark that we prove a uniqueness result for the homogeneous nonlinearity (mu = 0), which is based on the Morse index of ground state solutions.
资助项目	Fundamental Research Funds for the Central Universities[531118010205] ; National Natural Science Foundation of China[11771428] ; National Natural Science Foundation of China[11926335]
WOS研究方向	Mathematics
语种	英语
出版者	SPRINGER HEIDELBERG
WOS记录号	WOS:000562758200002
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/52021]
专题	数学所
通讯作者	Zhang, Zhitao
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, HLM, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.Hunan Univ, Sch Math, Changsha 410082, Hunan, Peoples R China
推荐引用方式 GB/T 7714	Luo, Haijun,Zhang, Zhitao. Normalized solutions to the fractional Schrodinger equations with combined nonlinearities[J]. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS,2020,59(4):35.
APA	Luo, Haijun,&Zhang, Zhitao.(2020).Normalized solutions to the fractional Schrodinger equations with combined nonlinearities.CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS,59(4),35.
MLA	Luo, Haijun,et al."Normalized solutions to the fractional Schrodinger equations with combined nonlinearities".CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS 59.4(2020):35.