CLASSIFICATION OF NONNEGATIVE SOLUTIONS TO STATIC SCHRODINGER-HARTREE-MAXWELL TYPE EQUATIONS

doi:10.1137/20M1341908

CSpace

	CLASSIFICATION OF NONNEGATIVE SOLUTIONS TO STATIC SCHRODINGER-HARTREE-MAXWELL TYPE EQUATIONS
	Dai, Wei 1,2; Liu, Zhao 3,4; Qin, Guolin 5,6
	2021
发表期刊	SIAM JOURNAL ON MATHEMATICAL ANALYSIS
ISSN	0036-1410
卷号	53 期号:2 页码:1379-1410
摘要	In this paper, we are mainly concerned with the physically interesting static Schrodinger-Hartree-Maxwell type equations (-Delta)(s)u(x) = (1/vertical bar x vertical bar(sigma)*vertical bar u vertical bar(p))u(q) (x) in R-n involving higherorder or higher-order fractional Laplacians, where n >= 1, 0 < s := m + alpha/2 < n/2, m >= 0 is an integer, 0 < alpha <= 2, 0 < sigma < n, 0 < p <= 2n-sigma/n-2s, and 0 < q <= n+2s-sigma/n-2s. We first prove the super poly-harmonic properties of nonnegative classical solutions to the above PDEs, then show the equivalence between the PDEs and the following integral equations u(x) = integral(Rn) R-2s,R-n/vertical bar x-y vertical bar(n-2s) (integral(Rn) 1/vertical bar y-z vertical bar(sigma)u(p)(z)dz)u(q) (y)dy. Finally, we classify all nonnegative solutions to the integral equations via the method of moving spheres in integral form. As a consequence, we obtain the classification results of nonnegative classical solutions for the PDEs and hence derive the sharp constants for related Hardy-Littlewood-Sobolev inequalities. Our results completely improved the classification results in [4, 23, 24, 25, 44] to the full range of s, sigma, p, and q. In critical and supercritical-order cases (i.e., n/2 <= s := m + alpha/2 < +infinity), we also derive Liouville type theorems.
关键词	higher-order fractional Laplacians Schrodinger-Hartree-Maxwell equations classification of nonnegative solutions super poly-harmonic properties nonlocal nonlinearities the method of moving spheres
DOI	10.1137/20M1341908
收录类别	SCI
语种	英语
资助项目	National Natural Science Foundation of China[11971049] ; National Natural Science Foundation of China[11801237] ; National Natural Science Foundation of China[11926324] ; Fundamental Research Funds for the Central Universities ; State Scholarship Fund of China[201806025011] ; State Scholarship Fund of China[201808360005] ; Natural Foundation of Jiangxi Province[20202BABL211001]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000646035100006
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/58666
专题	中国科学院数学与系统科学研究院
通讯作者	Liu, Zhao
作者单位	1.Beihang Univ BUAA, Sch Math Sci, Beijing 100083, Peoples R China 2.Univ Sorbonne Paris Cite, Inst Galilee, UMR 7539, LAGA, F-93430 Villetaneuse, France 3.Jiangxi Sci & Technol Normal Univ, Sch Math & Comp Sci, Nanchang 330038, Jiangxi, Peoples R China 4.Yeshiva Univ, Dept Math, New York, NY 10033 USA 5.Chinese Acad Sci, Inst Appl Math, Beijing 100190, Peoples R China 6.Univ Chinese Acad Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Dai, Wei,Liu, Zhao,Qin, Guolin. CLASSIFICATION OF NONNEGATIVE SOLUTIONS TO STATIC SCHRODINGER-HARTREE-MAXWELL TYPE EQUATIONS[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS,2021,53(2):1379-1410.
APA	Dai, Wei,Liu, Zhao,&Qin, Guolin.(2021).CLASSIFICATION OF NONNEGATIVE SOLUTIONS TO STATIC SCHRODINGER-HARTREE-MAXWELL TYPE EQUATIONS.SIAM JOURNAL ON MATHEMATICAL ANALYSIS,53(2),1379-1410.
MLA	Dai, Wei,et al."CLASSIFICATION OF NONNEGATIVE SOLUTIONS TO STATIC SCHRODINGER-HARTREE-MAXWELL TYPE EQUATIONS".SIAM JOURNAL ON MATHEMATICAL ANALYSIS 53.2(2021):1379-1410.