[1] Pitaevskii Lev. Vortex lines in an imperfect Bose gas. Sov Phys JETP-USSR, 1961, 13(2):451-454 [2] Gaididei Y B, Rasmussen K O, Christiansen P L. Nonlinear excitations in two-dimensional molecular structures with impurities. Physical Review E, 1995, 52(3):2951-2962 [3] Menzala G P, Strauss W A. On a wave equation with a cubic convolution. J Differential Equations, 1982, 43:93-105 [4] Hidano K. Small data scattering and blow-up for a wave equation with a cubic convolution. Funkcialaj Ekvacioj, 2000, 43:559-588 [5] Mochizuki K. On small data scattering with cubic convolution nonlinearity. J Math Soc Japan, 1989, 41:143-160 [6] Ginibre J, Velo G. Scattering theory in the energy space for a class of Hartree equations//Nonlinear wave equations (Providence, RI, 1998), 29-60, Contemp Math, 263. Providence, RI:Amer Math Soc, 2000 [7] Nakanishi K. Energy scattering for Hartree equations. Math Res Lett, 1999, 6:107-118 [8] Miao C, Xu G, Zhao L. Global well-posedness and scattering for the energy-critical, defousing Hartree equation for radial data. J Funct Anal, 2007, 253:605-627 [9] Miao C, Wu Y, Xu G. Dynamics for the focusing, energy-critical nonlinear Hartree equation. Forum Math, 2015, 27(1):373-447 [10] Miao C, Zhang J, Zheng J. The defocusing energy-critical wave equation with a cubic convolution. Indiana University Mathematics Journal, 2014, 63:1-23 [11] Kenig C, Merle F. Global well-posedness, scattering, and blow-up for the energy critical focusing nonlinear wave equation. Acta Math, 2008, 201(2):147-212 [12] Ibrahim S, Masmoudi N, Nakanishi K. Scattering threshold for the focusing nonlinear Klein-Gordon equation. Anal PDE, 2011, 4(3):405-460 [13] Ibrahim S, Masmoudi N, Nakanishi K. Threshold solutions in the case of mass-shift for the critical KleinGordon equation. Trans Amer Math Soc, 2014, 366(11):5653-5669 [14] Keel M, Tao T. Endpoint Strichartz estimates. Amer J Math, 1998, 120(5):955-980 [15] Li D, Miao C, Zhang X. The focusing energy-critical Hartree equation. J Differ Equt, 2009, 246:1139-1163 [16] Lieb E H, Loss M. Analysis. Graduate Studies in Mathematics, 2001 [17] Miao C, Xu G, Zhao L. Global well-posedness and scattering for the defocusing H1/2 -subcritical Hartree equation in Rd. Ann I H Poincare-AN, 2009, 26:1831-1852 [18] Miao C, Xu G, Zhao L. Global well-posedness and scattering for the mass-critical Hartree equation with radial data. Journal de Mathématiques Pures et Appliquées, 2009, 91:49-79 [19] Miao C, Xu G, Zhao L. Global well-posedness, scattering and blow-up for the energy-critical, focusing Hartree equation in the radial case. Colloquium Mathematicum, 2008, 114(2):213-236 [20] Miao C, Xu G, Zhao L. On the blow-up phenomenon for the mass-critiacl focusing Hartree equation in R4. Colloquium Mathematicum. 2010, 119(1):23-50 [21] Miao C, Xu G, Zhao L. Global well-posedness and scattering for the energy-critical, defocusing Hartree equation in R1+n. Communications in Partial Differential Equations, 2011, 36:729-776 [22] Miao C, Zhang B, Fang D. Global well-posedness for the Klein-Gordon equations below the energy norm. Journal of Partial Differential Equations, 2004, 17(2):97-121 [23] Nakanishi K. Remarks on the energy scattering for nonlinear Klein-Gordon and Schröinger equations. Tohoku Math J (2), 2001, 53(2):285-303 [24] Payne L E, Sattinger D H. Saddle points and instability of nonlinear hyperbolic equations. Israel J Math, 1975, 22:272-303 [25] Guo Q, Zhu S. Sharp threshold of blow-up and scattering for the fractional Hartree equation. J Differential Equations, 2018, 264(4):2802-2832 [26] Zhu S. On the blow-up solutions for the nonlinear fractional Schrödinger equation. J Differential Equations, 2016, 261(2):1506-1531 [27] Feng B. On the blow-up solutions for the nonlinear Schrödinger equation with combined power-type nonlinearities. J Evol Equ, 2018, 18(1):203-220 [28] Feng B. On the blow-up solutions for the fractional nonlinear Schrödinger equation with combined powertype nonlinearities. Commun Pure Appl Anal, 2018, 17(5):1785-1804 |