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Original Articles

Existence and concentrate behavior of positive solutions for Chern–Simons–Schrödinger systems with critical growth

, &
Pages 476-486 | Received 03 Aug 2019, Accepted 13 Jan 2020, Published online: 12 Feb 2020

References

  • Jackiw R, Pi S-Y. Self-dual Chern–Simons solitons. Prog Theor Phys Supp. 1992;107:1–40. doi: 10.1143/PTPS.107.1
  • Jackiw R, Pi S-Y. Classical and quantal nonrelativistic Chern–Simons theory. Phys Rev D. 1990;42:3500–3513. doi: 10.1103/PhysRevD.42.3500
  • Jackiw R, Pi S-Y. Soliton solutions to the gauged nonlinear Schrödinger equation on the plane. Phys Rev Lett. 1990;64:2969–2972. doi: 10.1103/PhysRevLett.64.2969
  • Bergé L, de Bouard A, Saut J-C. Blowing up time-dependent solutions of the planar, Chern–Simons gauged nonlinear schrodinger equation. Nonlinearity. 1995;8:235–253. doi: 10.1088/0951-7715/8/2/007
  • Han J, Huh H, Seok J. Chern–Simons limit of the standing wave solutions for the Schrödinger equations coupled with a neutral scalar field. J Funct Anal. 2014;266:318–342. doi: 10.1016/j.jfa.2013.09.019
  • Liu B, Smith P, Tataru D. Local wellposedness of Chern-Simons-Schrödinger. Int Math Res Not IMRN. 6341–6398.
  • Dunne G. Self-dual Chern–Simons theories. vol. 36. New York: Springer Science & Business Media; 1995.
  • 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
  • Deng Y, Peng S, Shuai W. Nodal standing waves for a gauged nonlinear Schrödinger equation in R2. J Differ Equations. 2018;264:4006–4035. doi: 10.1016/j.jde.2017.12.003
  • Luo X. Multiple normalized solutions for a planar gauged nonlinear Schrödinger equation. Z Angew Math Phys. 2018;69:367. Art. 58, 17. doi: 10.1007/s00033-018-0952-7
  • Pomponio A, Ruiz D. Boundary concentration of a gauged nonlinear Schrödinger equation on large balls. Calc Var Partial Dif. 2015;53:289–316. doi: 10.1007/s00526-014-0749-2
  • Pomponio A, Ruiz D. A variational analysis of a gauged nonlinear Schrödinger equation. J Eur Math Soc (JEMS). 2015;17:1463–1486. doi: 10.4171/JEMS/535
  • Cunha PL, d'Avenia P, Pomponio A, Siciliano G. A multiplicity result for Chern-Simons-Schrödinger equation with a general nonlinearity. NoDEA Nonlinear Diff. 2015;22:1831–1850. doi: 10.1007/s00030-015-0346-x
  • Ji C, Fang F. Standing waves for the Chern-Simons-Schrödinger equation with critical exponential growth. J Math Anal Appl. 2017;450:578–591. doi: 10.1016/j.jmaa.2017.01.065
  • Wan Y, Tan J. 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
  • 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
  • Berestycki H, Lions P-L. Nonlinear scalar field equations. I. Existence of a ground state. Arch Rational Mech Anal. 1983;82:313–345. doi: 10.1007/BF00250555
  • Chen S, Zhang B, Tang X. Existence and concentration of semiclassical ground state solutions for the generalized Chern-Simons-Schrödinger system in H1(R2). Nonlinear Anal. 2019;185:68–96. doi: 10.1016/j.na.2019.02.028
  • Wan Y, Tan J. The existence of nontrivial solutions to Chern-Simons-Schrödinger systems. Discrete Contin Dyn Syst. 2017;37:2765–2786. doi: 10.3934/dcds.2017119
  • Jeanjean L, Le Coz S. An existence and stability result for standing waves of nonlinear Schrödinger equations. Adv Differential Equ. 2006;11:813–840.
  • Cao DM. Nontrivial solution of semilinear elliptic equation with critical exponent in R2. Commun Part Diff Eq. 1992;17:407–435. doi: 10.1080/03605309208820848
  • do Ó JM. N-Laplacian equations in RN with critical growth. Abstr Appl Anal. 1997;2:301–315. doi: 10.1155/S1085337597000419
  • do Ó JM, Medeiros E, Severo U. A nonhomogeneous elliptic problem involving critical growth in dimension two. J Math Anal Appl. 2008;345:286–304. doi: 10.1016/j.jmaa.2008.03.074
  • Gilbarg D, Trudinger NS. Elliptic partial differential equations of second order. Berlin: Springer-Verlag; 2001. (Classics in Mathematics). Reprint of the 1998 edition.
  • Azzollini A, d'Avenia P, Pomponio A. On the Schrödinger-Maxwell equations under the effect of a general nonlinear term. Ann Inst H Poincaré Anal Non Linéaire. 2010;27:779–791. doi: 10.1016/j.anihpc.2009.11.012
  • Kikuchi H. Existence and stability of standing waves for Schrödinger-Poisson-Slater equation. Adv Nonlinear Stud. 2007;7:403–437. doi: 10.1515/ans-2007-0305
  • Willem M. Minimax theorems. Boston (MA): Birkhäuser Boston, Inc; 1996. (vol. 24 of Progress in Nonlinear Differential Equations and their Applications).

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