[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 |