References
- Jackiw R, Pi SY. Soliton solutions to the gauged nonlinear Schrödinger equations. Phys Rev Lett. 1990;64:2969–2972. doi: 10.1103/PhysRevLett.64.2969
- Jackiw R, Pi SY. Classical and quantal nonrelativistic Chern-Simons theory. Phys Rev D. 1990;42:3500–3513. doi: 10.1103/PhysRevD.42.3500
- Jackiw R, Pi SY. Self-dual Chern-Simons solitons. Progr Theoret Phys Suppl. 1992;107:1–40. doi: 10.1143/PTPS.107.1
- Byeon J, Huh H, Seok J. Standing waves of nonlinear Schrödinger equations with the gauge field. J Funct Anal. 2012;263:1575–1608. doi: 10.1016/j.jfa.2012.05.024
- Byeon J, Huh H, Seok J. On standing waves with a vortex point of order N for the nonlinear Chern-Simons-Schrödinger equations. J Diffe Equ. 2016;261:1285–1316. doi: 10.1016/j.jde.2016.04.004
- Huh H. Standing waves of the Schrödinger equation coupled with the Chern-Simons gauge field. J Math Phys. 2012;53:063702.
- Jiang Y, Pomponio A, Ruiz D. Standing waves for a Gauged Nonlinear Schrödinger equation with a vortex point. Commun Contemp Math. 2016;18:1550074. doi: 10.1142/S0219199715500741
- Pomponio A, Ruiz D. A variational analysis of a gauged nonlinear Schrödinger equation. J Eur Math Soc. 2015;17:1463–1486. doi: 10.4171/JEMS/535
- Ruiz D. The Schrödinger-Poisson equation under the effect of a nonlinear local term. J Funct Anal. 2006;237:655–674. doi: 10.1016/j.jfa.2006.04.005
- Li GB, Luo X. Normalized solutions for the Chern-Simons-Schrodinger equation in R2. Ann Acad Sci Fenn Math. 2017;42:405–428. doi: 10.5186/aasfm.2017.4223
- Li GB, Luo X, Shuai W. Sign-changing solutions to a gauged nonlinear Schrödinger equation. J Math Anal App. 2017;455:1559–1578. doi: 10.1016/j.jmaa.2017.06.048
- Zhang J, Tang XH, Zhang W. Existence and concentration of solutions for the Chern-Simons-Schrödinger system with general nonlinearity. Results Math. 2017;71:643–655. doi: 10.1007/s00025-016-0553-8
- Zhang J, Zhang W, Xie X. Infinitely many solutions for a gauged nonlinear Schrödinger equation. Appl Math Lett. 2019;88:21–27. doi: 10.1016/j.aml.2018.08.007
- Dunne V. Self-dual chern-simons theories. Berlin: Springer-Verlag; 1995.
- Pomponio A, Ruiz D. Boundary concentration of a Gauged nonlinear Schrödinger equation on large balls. Calc Var Partial Diffe Equ. 2015;53:289–316. doi: 10.1007/s00526-014-0749-2
- Wang Z, Zhou H. Positive solution for a nonlinear stationary Schrödinger-Poisson system in R3. Discrete Contin Dyn Syst. 2007;18:809–816. doi: 10.3934/dcds.2007.18.121
- Wan YY, Tan JG. Standing waves for the Chern-Simons-Schrödinger systems without (AR) condition. J Math Anal Appl. 2014;415:422–434. doi: 10.1016/j.jmaa.2014.01.084
- Berestycki H, Lions PL. Nonlinear scalar field equations. I. Existence of a ground state. Arch Rational Mech Anal. 1983;82:313–345. doi: 10.1007/BF00250555
- Cunha PL, D'avenia P, Pomponio A, et al. A multiplicity result for Chern-Simons-Schrödinger equation with a general nonlinearity. Nonli Diffe Equ Appl. 2015;22:1381–1850. doi: 10.1007/s00030-015-0326-1
- Bergé L, de Bouard A, Saut JC. Blowing up time-dependent solutions of the planar Chern-Simons gauged nonlinear Schrödinger equation. Nonlinearity. 1995;8:235–253. doi: 10.1088/0951-7715/8/2/007
- Huh H. Blow-up solutions of the Chern-Simons-Schrödinger equations. Nonlinearity. 2009;22:967–974. doi: 10.1088/0951-7715/22/5/003
- Huh H. Energy solution to the Chern-Simons-Schrödinger equations. Abstr Appl Anal. 2013, Article ID 590653.
- Liu B, Smith P. Global wellposedness of the equivariant Chern-Simons-Schrödinger equation. preprint arXiv:1312.5567.
- Liu B, Smith P, Tataru D. Local wellposedness of Chern-Simons-Schrödinger. Int Math Res Notices. doi:10.1093/imrn/rnt161.
- Zhang J, Zhang W, Tang XH. Ground state solutions for Hamiltonian elliptic system with inverse square potential. Discrete Contin Dyn Syst. 2017;37:4565–4583. doi: 10.3934/dcds.2017195
- Bartsch T, Wang ZQ. Existence and multiplicity results for some superlinear elliptic problems on RN. Comm Partial Diffe Equ. 1995;20:1725–1741. doi: 10.1080/03605309508821149
- Bartsch T, Pankov A, Wang ZQ. Nonlinear Schrödinger equations with steep potential well. Commun Contemp Math. 2001;3:549–569. doi: 10.1142/S0219199701000494
- Willem M. Minimax theorems. Berlin: Birkhäuser; 1996.
- Rabinowitz PH. Minimax methods in critical point theory with applications to differential equations. CBMS Reg. Conf. Ser. in Math. Vol. 65, Providence, RI: Amer. Math. Soc.; 1986.
- Tang XH, Lin XY. Infinitely many homoclinic orbits for Hamiltonian systems with indefinite sign subquadratic potentials. Nonlinear Anal. 2011;74:6314–6325. doi: 10.1016/j.na.2011.06.010