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Articles

Ground state solitary waves for the planar Schrödinger-Poisson system

Pages 1516-1527 | Received 19 Aug 2016, Accepted 16 Dec 2016, Published online: 06 Jan 2017

References

  • Lieb EH. Existence and uniqueness of minimizing solution of Choquard’s nonlinear equation. Stud Appl Math. 1977;57:93–105.
  • Lions PL. The Choquard equation and related questions. Nonlinear Anal. 1980;4:1063–1072.
  • Ambrosetti A, Ruiz D. Mutiple bounded states for the Schrödinger--Poisson problem. Commun Contemp Math. 2008;10:391–404.
  • Azzollini A, Pomponio A. Ground state solutions for the nonlinear Schrödinger--Maxwell equations. J Math Anal Appl. 2008;345:90–108.
  • Ruiz D, Siciliano G. A note on the Schrödinger--Poisson--Slater equation on bounded domains. Adv Nonlinear Stud. 2008;8:179–190.
  • Zhao L, Zhao F. On the existence of solutions for the Schrödinger--Poisson equations. J Math Anal Appl. 2008;346:155–169.
  • Mugnai D. The Schrödinger--Poisson system with positive potential. Commun Partial Differ Equ. 2011;36:1099–1117.
  • Cingolani S, Clapp M, Secchi S. Mutiple solutions to a magnetic nonlinear Choquard equation. Z Angew Math Phys. 2012;63:233–248.
  • Bellazzini J, Jeanjean L, Luo T. Existence and instability of standing waves with prescribed norm for a class of Schrödinger--Poisson equations. Proc Lond Math Soc. 2013;107:303–339.
  • Choquard P, Stubbe J, Vuffray M. Stationary solutions of the Schrödinger--Newton model-an ODE approach. Differ Integral Equ. 2008;21:665–679.
  • Cingolani S, Weth T. On the planar Schrödinger--Poisson system. Ann I H Poincare-AN; 2016;33:169–197.
  • Cazenave T, Lions PL. Orbital stability of standing waves for some nonlinear Schrödinger equations. Commun Math Phys. 1982;85:549–561.
  • Stubbe J. Bound states of two dimensional Schrödinger--Newton equations. 2008; arXiv:08074059.
  • Masaki S. Local existence and WKB approximation of solutions to Schrödinger--Poisson system in the two-dimensional whole space. Commun Partial Differ Equ. 2010;35:2253–2278.
  • Read M, Simon B. Methods of modern mathematical physics. Analysis of opetators. Vol. IV. New York (NY): Academic Press; 1978.
  • Lieb EH, Loss M. Analysis, 2nd ed., Graduate studies in mathematics. Vol. 13. Providence (RI): AMS; 2001.
  • Almgren FJ, Lieb EH. Symmetric decreasing rearrangement is sometimes continuous. J Amer Math Soc. 1989;2:683–773.
  • Struwe M. Variational methods. 2nd ed., Berlin: Springer-Verlag; 1996.
  • Ambrosi L, Gigli N, Savare G. Gradient flows in metric spaces and in the space of probability measures. 2nd ed., Birkhaüser Verlag; 2008.
  • Blanchet A, Calvez V, Carrillo JA. Convergence of the mass-transport steepest descent scheme for the subcricical Patlak--Keller--Segel model. SIAM J Numer Anal. 2008;46:691–721.

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