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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 467985, 5 pages
http://dx.doi.org/10.1155/2013/467985
Research Article

Nonexistence Results of Semilinear Elliptic Equations Coupled with the Chern-Simons Gauge Field

Department of Mathematics, Chung-Ang University, Seoul 156-756, Republic of Korea

Received 1 November 2012; Accepted 15 January 2013

Academic Editor: Khalil Ezzinbi

Copyright © 2013 Hyungjin Huh. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. J. Hong, Y. Kim, and P. Y. Pac, “Multivortex solutions of the abelian Chern-Simons-Higgs theory,” Physical Review Letters, vol. 64, no. 19, pp. 2230–2233, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. R. Jackiw and E. J. Weinberg, “Self-dual Chern-Simons vortices,” Physical Review Letters, vol. 64, no. 19, pp. 2234–2237, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. D. Chae and O. Yu. Imanuvilov, “The existence of non-topological multivortex solutions in the relativistic self-dual Chern-Simons theory,” Communications in Mathematical Physics, vol. 215, no. 1, pp. 119–142, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. H. Chan, C.-C. Fu, and C.-S. Lin, “Non-topological multi-vortex solutions to the self-dual Chern-Simons-Higgs equation,” Communications in Mathematical Physics, vol. 231, no. 2, pp. 189–221, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. K. Choe, “Multiple existence results for the self-dual Chern-Simons-Higgs vortex equation,” Communications in Partial Differential Equations, vol. 34, no. 10–12, pp. 1465–1507, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. M. Nolasco, “Nontopological N-vortex condensates for the self-dual Chern-Simons theory,” Communications on Pure and Applied Mathematics, vol. 56, no. 12, pp. 1752–1780, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  7. R. Wang, “The existence of Chern-Simons vortices,” Communications in Mathematical Physics, vol. 137, no. 3, pp. 587–597, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. R. M. Chen and D. Spirn, “Symmetric Chern-Simons-Higgs vortices,” Communications in Mathematical Physics, vol. 285, no. 3, pp. 1005–1031, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. J. Han and N. Kim, “Nonself-dual Chern-Simons and Maxwell-Chern-Simons vortices on bounded domains,” Journal of Functional Analysis, vol. 221, no. 1, pp. 167–204, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. J. Han and N. Kim, “Corrigendum: nonself-dual Chern-Simons and Maxwell-Chern-Simons vortices on bounded domains,” Journal of Functional Analysis, vol. 242, no. 2, p. 674, 2007.
  11. R. Jackiw and S.-Y. Pi, “Classical and quantal nonrelativistic Chern-Simons theory,” Physical Review, vol. 42, no. 10, pp. 3500–3513, 1990. View at Publisher · View at Google Scholar · View at MathSciNet
  12. G. V. Dunne, Self-Dual Chern-Simons Theories, 1995.
  13. P. A. Horvathy and P. Zhang, “Vortices in (abelian) Chern-Simons gauge theory,” Physics Reports, vol. 481, no. 5-6, pp. 83–142, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  14. J. Byeon, H. Huh, and J. Seok, “Standing waves of nonlinear Schrödinger equations with the gauge field,” Journal of Functional Analysis, vol. 263, no. 6, pp. 1575–1608, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. H. Huh, “Standing waves of the Schrodinger equation coupled with the Chern-Simons gauge field,” Journal of Mathematical Physics, vol. 53, no. 6, Article ID 063702, 8 pages, 2012. View at Publisher · View at Google Scholar
  16. H. Berestycki and P.-L. Lions, “Nonlinear scalar field equations. I. Existence of a ground state,” Archive for Rational Mechanics and Analysis, vol. 82, no. 4, pp. 313–345, 1983. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet