SYMMETRY OF POSITIVE SOLUTIONS FOR THE FRACTIONAL HARTREE EQUATION

doi:10.1007/s10473-019-0603-x

Abstract

CLC Number:

35R11

Xiangqing Liu. SYMMETRY OF POSITIVE SOLUTIONS FOR THE FRACTIONAL HARTREE EQUATION[J].Acta mathematica scientia,Series B, 2019, 39(6): 1508-1516.

Trendmd

[1] Chen W, Fang Y, Yang R. Liouville theorems involving the fractional Laplacian on a half space. Adv Math, 2015, 274:167-198
[2] Chen W, Li C, Li Y. A direct method of moving planes for the fractional Laplacian. Adv Math, 2017, 308:404-437
[3] Chen W, Li Y, Zhang R. A direct method of moving planes on fractional order equations. J Funct Anal, 2017, 272:4131-4157
[4] Serrin J. A symmetry problem in potential theory. Arch Ration Mech Anal, 1971, 43:304-318
[5] Dai W, Fang Y Q, Qin G L. Classification of positive solutions to fractional order Hartree equations via a direct method of moving planes. J Differential Equations, 2018, 265:2044-2063
[6] Dai W, Fang Y, Huang J, Qin Y, Wang B. Regularity and classification of solutions to static Hartree equations involving fractional Laplacians. Discrete and Continuous Dynamical Systems, 2019, 39(3):1389-1403
[7] Lieb E, Simon B. The Hartree-Fock theory for Coulomb systems. Commun Math Phys, 1977, 53:185-194
[8] Cabré X, Sire Y. Nonlinear equations for fractional Laplacians, I:regularity, maximum principles, and Hamiltonian estimates. Ann Inst Henri Poincaré Anal Non Linéaire, 2014, 31:23-53
[9] Fröhlich J, Jonsson B L G, Lenzmann E. Boson stars as solitary waves. Commun Math Phys, 2007, 274(1):1-30
[10] Fröhlich J, Lenzmann E. Mean-field limit of quantum bose gases and nonlinear Hartree equation. In:Sminaire E D P, 2003-2004, Exp XIX:26pp
[11] Lei Y. Qualitative analysis for the Hartree-type equations. SIAM J Math Anal, 2013, 45:388-406
[12] Lieb E H. Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities. Ann Math, 1983, 118(2):349-374
[13] Liu S. Regularity, symmetry, and uniqueness of some integral type quasilinear equations. Nonlin Anal, 2009, 71:1796-1806
[14] Li D, Miao C, Zhang X. The focusing energy-critical Hartree equation. J Differential Equations, 2009, 246:1139-1163
[15] Moroz V, Schaftingen J Van. Groundstates of nonlinear Choquard equations:existence, qualitative properties and decay asymptotics. J Funct Anal, 2013, 265:153-184
[16] Miao C, Xu G, Zhao L. Global well-posedness, scattering and blow-up for the energy-critical, focusing Hartree equation in the radial case. Colloq Math, 2009, 114:213-236
[17] Li X W, Liu Z H, Li J. Existence and controllability for nonlinear fractional control systems with damping in Hilbert spaces. Acta Math Sci, 2019, 39B(1):229-242

SYMMETRY OF POSITIVE SOLUTIONS FOR THE FRACTIONAL HARTREE EQUATION

PDF (PC)

Abstract

Cite this article

share this article

References

Related Articles 15

Metrics

Comments

Recommended 9

[1]	Vladas SKAKAUSKAS. SOLVABILITY OF A NONLINEAR PROBLEM ARISING IN REACTIONS OVER INHOMOGENEOUS SURFACES [J]. Acta mathematica scientia,Series B, 2019, 39(5): 1380-1396.
[2]	Panpan REN, Jiang-Lun WU. LEAST SQUARES ESTIMATOR FOR PATH-DEPENDENT MCKEAN-VLASOV SDES VIA DISCRETE-TIME OBSERVATIONS [J]. Acta mathematica scientia,Series B, 2019, 39(3): 691-716.
[3]	Jinghui QIU. VECTORIAL EKELAND VARIATIONAL PRINCIPLE AND CYCLICALLY ANTIMONOTONE EQUILIBRIUM PROBLEMS [J]. Acta mathematica scientia,Series B, 2019, 39(2): 524-544.
[4]	Jiankai XU, Zhong TAN, Weiwei WANG, Zepeng XIONG. A NECESSARY CONDITION FOR CERTAIN INTEGRAL EQUATIONS WITH NEGATIVE EXPONENTS [J]. Acta mathematica scientia,Series B, 2019, 39(1): 284-296.
[5]	Pengyan WANG, Yongzhong WANG. POSITIVE SOLUTIONS FOR A WEIGHTED FRACTIONAL SYSTEM [J]. Acta mathematica scientia,Series B, 2018, 38(3): 935-949.
[6]	Huifang JIA, Gongbao LI. MULTIPLICITY AND CONCENTRATION BEHAVIOUR OF POSITIVE SOLUTIONS FOR SCHRÖDINGER-KIRCHHOFF TYPE EQUATIONS INVOLVING THE p-LAPLACIAN IN R^N [J]. Acta mathematica scientia,Series B, 2018, 38(2): 391-418.
[7]	Jiafeng LIAO, Yang PU, Chunlei TANG. MULTIPLICITY OF POSITIVE SOLUTIONS FOR A CLASS OF CONCAVE-CONVEX ELLIPTIC EQUATIONS WITH CRITICAL GROWTH [J]. Acta mathematica scientia,Series B, 2018, 38(2): 497-518.
[8]	Ruyun MA, Hongliang GAO. MULTIPLE POSITIVE SOLUTIONS FOR A CLASS OF SEMIPOSITONE NEUMANN PROBLEMS WITH SINGULAR φ-LAPLACIAN [J]. Acta mathematica scientia,Series B, 2017, 37(5): 1472-1482.
[9]	Wei DAI, Zhao LIU. CLASSIFICATION OF POSITIVE SOLUTIONS TO A SYSTEM OF HARDY-SOBOLEV TYPE EQUATIONS [J]. Acta mathematica scientia,Series B, 2017, 37(5): 1415-1436.
[10]	Yanyan GUO. NONEXISTENCE AND SYMMETRY OF SOLUTIONS TO SOME FRACTIONAL LAPLACIAN EQUATIONS IN THE UPPER HALF SPACE [J]. Acta mathematica scientia,Series B, 2017, 37(3): 836-851.
[11]	Wanzhong GONG, Daoxiang ZHANG. MONOTONICITY IN ORLICZ-LORENTZ SEQUENCE SPACES EQUIPPED WITH THE ORLICZ NORM [J]. Acta mathematica scientia,Series B, 2016, 36(6): 1577-1589.
[12]	Yan LI. NONEXISTENCE OF POSITIVE SOLUTIONS FOR A SEMI-LINEAR EQUATION INVOLVING THE FRACTIONAL LAPLACIAN IN R^N [J]. Acta mathematica scientia,Series B, 2016, 36(3): 666-682.
[13]	WEI Zhong-Li. SOME NECESSARY AND SUFFICIENT CONDITIONS FOR EXISTENCE OF POSITIVE SOLUTIONS FOR THIRD ORDER SINGULAR SUBLINEAR MULTI-POINT BOUNDARY VALUE PROBLEMS [J]. Acta mathematica scientia,Series B, 2014, 34(6): 1795-1810.
[14]	FAN Hai-Ning, LIU Xiao-Chun. MULTIPLE POSITIVE SOLUTIONS FOR A CLASS OF QUASI-LINEAR ELLIPTIC EQUATIONS INVOLVING CRITICAL SOBOLEV EXPONENT [J]. Acta mathematica scientia,Series B, 2014, 34(4): 1111-1126.
[15]	Tsing-San HSU. MULTIPLE POSITIVE SOLUTIONS FOR QUASILINEAR ELLIPTIC PROBLEMS INVOLVING CONCAVE-CONVEX NONLINEARITIES AND MULTIPLE HARDY-TYPE TERMS [J]. Acta mathematica scientia,Series B, 2013, 33(5): 1314-1328.