|   [1] Br´ezis H, Lieb E H. Minimum action solutions of some vector field equations. Comm Math Phys, 1984, 96: 97–113 
 
[2] Cycon H L, Froese R G, KirschW, Simon B. Schr¨odinger operators and application to quantum mechanics and global geometry//Texts and Monograghs in Physics. Berlin: Springer-Verlag, 1987 
 
[3] Carles R. Changing blow-up time in nonlinear Schr¨odinger equations. Journ´es ´Equations aux d´eriv´es partielles, Forges-les-Eaux, 2003: GDR2434 
 
[4] Carles R, Nakamura Y. Nonlinear Schr¨odinger equations with stark potential. Hokkaido Math J, 2004, 33: 719–729 
 
[5] Cazenave T. Semilinear Schr¨odinger Equations. Courant Lecture Notes in Mathematics, 10. Courant Inst of Math Sci, Amer Math Soc, 2003 
 
[6] de Bouard A. Nonlinear Schr¨odinger equations with magnetic fields. Differential Integral Equations, 1991, 4: 73–88 
 
[7] Fibich G, Merle F, Rapha¨el P. Numerical proof of a spectral property related to singularity formulation for the L2 critical nonlinear Schr¨odinger equation. Physic D, 2006, 220: 1–13 
 
[8] Ginibre J, Velo G. On a class of nonlinear Schr¨odinger equations. I. The Cauchy problem, general case. J Funct Anal, 1979, 32: 1–32 
 
[9] Glassey R T. On the blowing up of solutions to the Cauchy problem for nonlinear Schr¨odinger equations. J Math Phys, 1977, 18: 1794–1797 
 
[10] Kwong M K. Uniqueness of positive solutions of △u−u+up = 0 in Rn. Arch Rational Mech Anal, 1989, 105: 243–266 
 
[11] Lieb E H. On the lowest eigenvalue of the Laplacian for the intersection of two domains. Invent Math, 1983, 74: 441–448 
 
[12] Lions P L. The concentration-compactness principle in the calculus of variations. The locally compact case. I. Ann Inst H Poincar´e Anal Non Lin´eaire, 1984, 1: 109–145 
 
[13] Lions P L. The concentration-compactness principle in the calculus of variations. The locally compact case. II. Ann Inst H Poincaré Anal Non Linéaire, 1984, 1: 223–283 
 
[14] Li X G, Zhu S H. Blow-up rate for critical nonlinear Schr¨odinger equation with stark potential. Applicable Analysis, 2008, 87: 303–310 
 
[15] Joly J L, M´etivier G, Rauch J. Diffractive nonlinear geometric optics with rectification. Indiana Univ Math J, 1998, 47: 1167–1241 
 
[16] Merle F, Tsutsumi Y. L2 concentration of blow up solutions for the nonlinear Schr¨odinger equation with critical power nonlinearity. J Diff Equ, 1990, 84: 205–214 
 
[17] Glangetas L, Merle F. Concentration properties of blow-up solutions and instability results for Zakharov equation in dimension two, Part II. Comm Math Phys, 1994, 160: 349–389 
 
[18] Nakamura, Y. On nonlinear Schr¨odinger equations with Stark effect. Preprint, 2002 
 
[19] Nawa H. Asymptotic and limiting profiles of blowup solutions of the nonlinear Schr¨odinger equation with critical power. Comm Pure Appl Math, 1999, 52(2): 193–270 
 
[20] Merle F, Raphäel P. Blow-up dynamic and upper bound on the blow-up rate for critical nonlinear Schr¨odinger equation. Ann Math, 2005, 161: 157–222 
 
[21] Merle F, Raphäel P. On a sharp lower bound on the blow-up rate for the L2-critical nonlinear Schr¨odinger equation. J Amer Soc, 2006, 19: 37–90 
 
[22] Merle F, Raphäel P. Profiles and quantization of the blowup mass for critical nonlinear Schr¨odinger equation. Comm Math Phys, 2005, 253: 675–672 
 
[23] Nakamura Y. Local solvability and smoothing effects of nonlinear Schr¨odinger equations with magnetic fields. Funkcial Ekvac, 2001, 44: 1–18 
 
[24] Ogawa T, Tsutsumi Y. Blow-up of H1 solution for the nonlinear Schr¨odinger equation. J Diff Equ, 1991, 92: 317–330 
 
[25] Ozawa T. Nonexistence of wave operators with Stark effect Hamiltonians. Math Z, 1991, 207: 335–339 
 
[26] Ozawa T. Space-time behavior of propagators for Schr¨odinger evolution equations with Stark effect. J Funct Anal, 1991, 97: 264–292 
 
[27] Sulem C, Sulem P L. The Nonlinear Schr¨odinger Equation, Self-focusing and Wave Collapse. New York: Springer-Verlag, 1999 
[28] Strauss W A. Existence of solitary waves in higher dimensions. Comm Math Phys, 1977, 55: 149–162 
 
[29] Tsutsumi Y. Rate of L2 concentration of blowup solutions for the nonlinear Schr¨odinger equation with critical nonlinearity. Nonlinear Anal, 1990, 15: 719–724 
 
[30] Weinstein M I. Nonlinear Schr¨odinger equations and sharp interpolation estimates. Comm Math Phys, 1983, 87: 567–576 
 
[31] Weinstein M I. On the structure and formation of singularities in solutions to nonlinear dispersive evolution equations. Comm Part Diff Equ, 1986, 11: 545–565 
 
[32] Tsurumi T, Wadati M. Free fall of atomic laser beam with weak inter-atomic interaction. J Phys Soc Japan, 2001, 70: 60–68 
 
[33] Yajiam Y. Existence of solutions for Schr¨odinger evolution equations. Comm Math Phys, 1987, 110: 415–426 
 
[34] Zhang J. Stability of attractive Bose-Einstein condensate. J Statist Phys, 2000, 101: 731–746 
 
[35] Zhang J. Sharp conditions of global existence for nonlinear Schr¨odinger and Klein-Gordon equations. Nonlinear Anal, 2002, 48: 191–207  |