Xincai ZHU
. EXISTENCE AND BLOW-UP BEHAVIOR OF CONSTRAINED MINIMIZERS FOR SCHRÖDINGER-POISSON-SLATER SYSTEM[J]. Acta mathematica scientia, Series B, 2018
, 38(2)
: 733
-744
.
DOI: 10.1016/S0252-9602(18)30777-X
[1] Ambrosetti A, Ruiz D. Multiple bounded states for Schrödinger-Poisson problem. Comm Contemp Math, 2008, 10(3):391-404
[2] Bellazzini J, Siciliano G. Scaling properties of functionals and existence of constrained minimizers. J Funct Anal, 2011, 261(9):2486-2507
[3] Bokanowski O, Lopez J L, Soler J. On an exchange interaction model for quantum transport:the Schrödinger-Poisson-Slater system. Math Models Methods Appl Sci, 2003, 13(10):1397-1412
[4] Brézis H, Lieb E H. A relation between pointwise convergence of functions and convergence of functionals. Proc Amer Math Soc, 1983, 88(3):486-490
[5] Cao D M, Su Y M. Minimal blow-up solutions of mass-critical inhomogeneous Hartee equation. J Math Phys, 2013, 54(12):121511
[6] Catto I, Dolbeault J, Sánchez O, Soler J. Existence of steady states for the Maxwell-Schrödinger-Poisson system:exploring the applicability of the concentration-compactness principle. Math Models Methods Appl Sci, 2013, 23(10):1915-1938
[7] Guo Y J, Seiringer R. On the mass concentration for Bose-Einstein condensates with attactive interactions. Lett Math Phys, 2014, 104(2):141-156
[8] Guo Y J, Wang Z Q, Zeng X Y, Zhou H S. Properties of ground states of attractive Gross-Pitaevskii equations with multi-well potentials. arXiv:1502.01839, submitted, 2015
[9] Guo Y J, Zeng X Y, Zhou H S. Energy estimates and symmetry breaking in attactive Bose-Einstein condensates with ring-shaped potentials. Ann Inst H Poincaré Anal Non Linéaire, 2016, 33(3):809-828
[10] Jeanjean L, Luo T J. Sharp nonexistence results of prescribed L2-norm solutions for some class of Schrödinger-Poisson and quasi-linear equations. Z Angew Math Phys, 2013, 64(4):937-954
[11] Kikuchi H. On the existence of a solution for elliptic system related to Maxwell-Schrödinger equations. Nonlinear Anal, 2007, 67(5):1445-1456
[12] Kwong M K. Uniqueness of positive solutions of △u-u + up=0 in RN. Arch Rational Mech Anal, 1989, 105(3):243-266
[13] Lieb E H. Existence and uniqueness of the minimizing solution of choquard's nonlinear equation. Stud Appl Math, 1977, 57(2):93-105
[14] Lions P L. The Choquard equation and related questions. Nonlinear Anal, 1980, 4(6):1063-1072
[15] Lions P L. The concentration-compactness principle in the caclulus of variations. The locally compact case. I. Ann Inst H Poincaré Anal Non Linéaire, 1984, 1(2):109-145
[16] Lions P L. The concentration-compactness principle in the caclulus of variations. The locally compact case. Ⅱ. Ann Inst H Poincaré Anal Non Linéaire, 1984, 1(4):223-283
[17] Li Y, Ni W M. Radial symmetry of positive solutions of nonlinear elliptic equations in Rn. Comm Partial Differential Equations, 1993, 18(5-6):1043-1054
[18] Penrose R. On Gravity's role in Quantum State Reduction. Gen Relativity Gravitation, 1996, 28(5):581-600
[19] Sánchez O, Soler J. Long-Time Dynamics of the Schrödinger-Poisson-Slater System. J Stat Phys, 2004, 114(1):179-204
[20] Weinstein M I. Nonlinear Schrödinger equations and sharp interpolations estimates. Comm Math Phys, 1983, 87(4):567-576
[21] Willem M. Minimax theorems. Springer Science & Business Media, 1997
[22] Xiang C L. Quantitative properties on the steady states to a Schrödinger-Poisson-Slater system. Acta Math Sin English Ser, 2015, 31(12):1845-1856
[23] Zhao L G, Zhao F K. On the existence of solutions for the Schrödinger-Poisson equations. J Math Anal Appl, 2008, 346(1):155-169
